Size-dependent continuum-based model of a truncated flexoelectric/flexomagnetic functionally graded conical nano/microshells

Abstract

In this study, in the presence of a magnetic field using a continuous electromechanical model based on the first-order shear deformation shell model and a modified flexoelectric theory, a new formulation is introduced to study the electromechanical behavior of flexoelectric materials. To improve the internal energy function for isotropic materials, the coupling equations governing the functionally graded magneto-electro-elastic (FGMEE) conical nanoshell have been examined. After extracting the governing equations of the flexoelectric functionally graded conical nanoshell, the corresponding boundary conditions of the coupling equations between mechanical and electrical forces are presented. It should be noted that the formulation of the governing coupled equations of the FGMEE conical nanoshell with polarization independent of electrical potential is the underlying innovation of the current study. To demonstrate the capability and uniqueness of the formulation, static analysis and free vibrations of the shell have been investigated in particular states. To assess the extracted equations in this particular case, the shell equations along with the relevant boundary conditions are solved using Galerkin and the numerically developed Kantorovich method. Finally, various effects including the effect of size and geometric dimensions on the vibration frequency and static analysis have been examined.

Appendices

Appendix 1

According to the definition, the physical components of the strain gradient tensor are as follows:

$$\eta _{{{\text{ijk}}}} = \varepsilon _{{{\text{jk}},i}} = \frac{1}{2}\left( {\left. {u_{j} } \right|_{{{\text{ki}}}} + \left. {u_{k} } \right|_{{{\text{ji}}}} } \right).$$

(69)

In relations pertaining to the orthogonal curvilinear coordinate system, we have [83]:

$$\begin{gathered} {\left. {u_j} \right|_{{\text{ki}}}} = {u_{j,{\text{ki}}}} - {(\Gamma_{j\,\,\,k}^m)_{,i}}{u_m} - \Gamma_{j\,\,\,k}^m{({u_m})_{,i}} - \Gamma_{j\,\,\,i}^s{({u_s})_{,k}} - \Gamma_{k\,\,\,i}^s{({u_j})_{,s}} \hfill \\ + \Gamma_{j\,\,\,i}^s\Gamma_{s\,\,\,k}^m{u_m} + \Gamma_{k\,\,\,i}^s\Gamma_{j\,\,\,s}^m{u_m} \hfill \\ \end{gathered}$$

(70)

where ${\left. {u_j} \right|_{{\text{ki}}}}$ is the second-order deformation gradient tensor, g is the metric (Euclidean) tensor, and ${\Gamma }_{j\;k}^i$ is the Christoffel symbol, and the physical components of this tensor are defined as follows:

$$\begin{gathered} {u_{(j),{\text{ki}}}} = {({u_{(j)}}\sqrt {{g_{{\text{jj}}}}} )_{,{\text{ki}}}} - \Gamma_{j\,\,\,k}^m{({u_{(m)}}\sqrt {{g_{{\text{mm}}}}} )_{,i}} - \Gamma_{j\,\,\,i}^s{({u_{(s)}}\sqrt {{g_{{\text{ss}}}}} )_{,k}} \hfill \\ - \Gamma_{k\,\,\,i}^s{({u_{(j)}}\sqrt {{g_{{\text{jj}}}}} )_{,s}} + [ - {(\Gamma_{j\,\,\,k}^m)_{,i}} + \Gamma_{j\,\,\,i}^s\Gamma_{s\,\,\,k}^m + \Gamma_{k\,\,\,i}^s\Gamma_{j\,\,\,s}^m]({u_{(m)}}\sqrt {{g_{{\text{mm}}}}} ). \hfill \\ \end{gathered}$$

(71)

The definition of the physical components of the strain gradient tensor is as follows:

$${\eta_{({\text{ijk}})}} = \sqrt {{g^{{\text{ii}}}}} \sqrt {{g^{{\text{jj}}}}} \sqrt {{g^{{\text{kk}}}}} {\eta_{{\text{ijk}}}} = \frac{1}{{\sqrt {{g_{{\text{ii}}}}} \sqrt {{g_{{\text{jj}}}}} \sqrt {{g_{{\text{kk}}}}} }}{\eta_{{\text{ijk}}}}$$

(72)

In this relation, $g_{{{\text{ii}}}}$ are components which refer to Einstein’s summation notation and $g^{{{\text{ii}}}}$ is the conjugate of $g_{{{\text{ii}}}}$.

$$\begin{aligned} \sqrt {g_{{{\text{ii}}}} } & \sqrt {g_{{{\text{jj}}}} } \sqrt {g_{{{\text{kk}}}} } \eta _{{({\text{ijk}})}} = \frac{1}{2}(u_{{(j),{\text{ki}}}} + u_{{(k),{\text{ji}}}} ) \to \\ & \eta _{{({\text{ijk}})}} = \frac{1}{2}\frac{1}{{\sqrt {g_{{{\text{ii}}}} } \sqrt {g_{{{\text{jj}}}} } \sqrt {g_{{{\text{kk}}}} } }}(u_{{(j),{\text{ki}}}} + u_{{(k),{\text{ji}}}} ). \\ \end{aligned}$$

(73)

In the conical shell coordinate system, the nonzero components of the tensors ${\Gamma }_{k l}^{m}$ and ${g}_{kl}$ are calculated as follows:

$$\begin{gathered} g_{{xx}} = 1,g_{{\theta \theta }} = (x\sin \alpha (1 + z/x\tan \alpha ))^{2} ,g_{{zz}} = 1, \hfill \\ \Gamma _{{\theta x}}^{\theta } = \Gamma _{{x\theta }}^{\theta } = \frac{1}{{x(1 + z/x\tan \alpha )}},\Gamma _{{\theta \theta }}^{x} = - x\sin ^{2} \alpha (1 + z/x\tan \alpha ), \hfill \\ \Gamma _{{\theta \theta }}^{z} = - x\sin \alpha \cos \alpha (1 + z/x\tan \alpha ),\Gamma _{{\theta z}}^{\theta } = \Gamma _{{z\theta }}^{\theta } = \frac{1}{{x\tan \alpha (1 + z/x\tan \alpha )}}. \hfill \\ \end{gathered}$$

(74)

According to the relations (72), (73) and (74), the physical components of the tensor ${\eta_{ijk}}$ are obtained. Based on the definition of components of the symmetric part of the strain gradient tensor and the components of the deviatoric strain gradient tensor, the components of the deviatoric strain gradient tensor are defined as follows:

$$\eta_{{\text{ijk}}}^{(1)} = \frac{1}{3}({\eta_{{\text{ijk}}}} + {\eta_{{\text{jki}}}} + {\eta_{{\text{kij}}}}) - \frac{1}{5}({\delta_{{\text{ij}}}}\eta_{{\text{mmk}}}^s + {\delta_{{\text{jk}}}}\eta_{{\text{mmi}}}^s + {\delta_{{\text{ki}}}}\eta_{{\text{mmj}}}^s),\eta_{{\text{ijk}}}^s = \frac{1}{3}({\eta_{{\text{ijk}}}} + {\eta_{{\text{jki}}}} + {\eta_{{\text{kij}}}}),$$

(75)

Similarly, the definition of the components of deviatoric strain gradient tensor, hydrostatic strain, and strain gradient tensor is as follows:

$$\begin{gathered} {{\chi ^{\prime}}_{{\text{ij}}}} = {e_{{\text{ipq}}}}{{\eta ^{\prime}}_{{\text{pqj}}}}. \hfill \\ {{\eta ^{\prime}}_{{\text{ijk}}}} = {\eta_{{\text{ijk}}}} - \eta_{{\text{ijk}}}^h. \hfill \\ \eta_{{\text{ijk}}}^h = \frac{1}{3}{\delta_{{\text{jk}}}}{\eta_{{\text{inn}}}}. \hfill \\ \end{gathered}$$

(76)

The deviatoric rotation gradient tensor components are obtained. In defining the components of the strain tensor deviatoric part and the components of the strain tensor [72], we have the following:

$$\varepsilon _{{xx}} = \frac{{\partial u}}{{\partial x}},\varepsilon _{{\theta \theta }} = \frac{1}{{x\sin \alpha (1 + z/x\tan \alpha )}}\left[ {\frac{{\partial v}}{{\partial \theta }} + u\sin \alpha + w\cos \alpha } \right],\varepsilon _{{zz}} = \frac{{\partial w}}{{\partial z}},$$

$$\varepsilon _{{x\theta }} = \varepsilon _{{\theta x}} = \frac{1}{{2x\sin \alpha (1 + z/x\tan \alpha )}}\left[ {\frac{{\partial u}}{{\partial \theta }} + x\sin \alpha (1 + z/x\tan \alpha )\frac{{\partial v}}{{\partial x}} - v\sin \alpha } \right],$$

$$\varepsilon _{{z\theta }} = \varepsilon _{{\theta z}} = \frac{1}{{2x\sin \alpha (1 + z/x\tan \alpha )}}\left[ {\frac{{\partial w}}{{\partial \theta }} + x\sin \alpha (1 + z/x\tan \alpha )\frac{{\partial v}}{{\partial z}} - v\cos \alpha } \right],$$

$$\varepsilon _{{xz}} = \varepsilon _{{zx}} = \frac{1}{2}\left[ {\frac{{\partial w}}{{\partial x}} + \frac{{\partial u}}{{\partial z}}} \right].$$

$${\varepsilon ^{\prime}_{{\text{ij}}}} = {\varepsilon_{{\text{ij}}}} - \frac{1}{3}{\delta_{{\text{ij}}}}{\varepsilon_{{\text{nn}}}}$$

(77)

Therefore, the components of the deviatoric part of strain tensor are obtained. The definition of the gradient components of a vector in an orthogonal curvilinear coordinate system is:

$${\left. {u^l} \right|_j} = \frac{{\partial {u^l}}}{{\partial {q^j}}} + \Gamma_{m\,\,\,j}^l{u^m}.$$

(78)

The dilatation gradient vector components are defined as follows:

$${\gamma_i} = {\left. {{\varepsilon_{nn}}} \right|_i} = {\left. {(\underline \nabla .\underline u )} \right|_i}.$$

(79)

Finally, according to the definition of the physical components of this coordinate system, the physical components of the dilatation gradient vector are obtained. Considering the physical components of the vector $\vec P$ the polarization vector and the vector $\vec M$ the magnetization vector in general and also according to the definition of the gradient of the vector of the curvilinear coordinate system, we will have:

$$\overrightarrow P = ({P_x}(x,\theta ,z,t),{P_\theta }(x,\theta ,z,t),{P_z}(x,\theta ,z,t)).$$

$${Q_{({\text{ij}})}} = \frac{1}{{\sqrt {{g_{{\text{ii}}}}} \sqrt {{g_{{\text{jj}}}}} }}\left[ {{{({P_{(i)}}\sqrt {{g_{{\text{ii}}}}} )}_{,j}} - \Gamma_{i\,j}^m{P_{(m)}}\sqrt {{g_{{\text{mm}}}}} } \right],$$

(80)

similarly:

$$\overrightarrow M = ({M_x}(x,\theta ,z,t),{M_\theta }(x,\theta ,z,t),{M_z}(x,\theta ,z,t)).$$

$${S_{({\text{ij}})}} = \frac{1}{{\sqrt {{g_{{\text{ii}}}}} \sqrt {{g_{{\text{jj}}}}} }}\left[ {{{({M_{(i)}}\sqrt {{g_{{\text{ii}}}}} )}_{,j}} - \Gamma_{i\,j}^m{M_{(m)}}\sqrt {{g_{{\text{mm}}}}} } \right],$$

(81)

Based on the Maxwell electric field definition (14) and the gradient definition of a vector in the orthogonal curvilinear coordinate system, we will have:

$$\begin{gathered} E_i^{{\text{MS}}} = - {\left. \varphi \right|_i},E_{(i)}^{{\text{MS}}} = \frac{ - 1}{{\sqrt {{g_{{\text{ii}}}}} }}\frac{\partial \varphi (x,\theta ,z,t)}{{\partial {q^i}}} \hfill \\ E_{(x)}^{{\text{MS}}} = - \frac{\partial \varphi (x,\theta ,z,t)}{{\partial x}},E_{(\theta )}^{{\text{MS}}} = \frac{ - 1}{{x\sin \alpha (1 + z/x\tan \alpha )}}\frac{\partial \varphi (x,\theta ,z,t)}{{\partial \theta }},E_{(z)}^{{\text{MS}}} = - \frac{\partial \varphi (x,\theta ,z,t)}{{\partial z}}. \hfill \\ \end{gathered}$$

(82)

In the same way, for the components of Maxwell magnetic flux field we will have:

$$\begin{gathered} H_{(i)}^{{\text{MS}}} = \frac{ - 1}{{\sqrt {{g_{{\text{ii}}}}} }}\frac{\partial \psi (x,\theta ,z,t)}{{\partial {q^i}}} \hfill \\ H_{(x)}^{{\text{MS}}} = - \frac{\partial \psi (x,\theta ,z,t)}{{\partial x}},H_{(\theta )}^{{\text{MS}}} = \frac{ - 1}{{x\sin \alpha (1 + z/x\tan \alpha )}}\frac{\partial \psi (x,\theta ,z,t)}{{\partial \theta }},H_{(z)}^{{\text{MS}}} = - \frac{\partial \psi (x,\theta ,z,t)}{{\partial z}}. \hfill \\ \end{gathered}$$

(83)

Appendix 2

The resultants of force and moments are defined as follows:

$$N_{f} = \int\limits_{{ - \frac{h}{2}}}^{{\frac{h}{2}}} f {\text{d}}z,M_{f} = \int\limits_{{ - \frac{h}{2}}}^{{\frac{h}{2}}} f \,z\,{\text{d}}z.$$

(84)

Also, consider the relation pertaining to the functionally graded behavior of the conical nanoshell as follows:

$$M(z) = M_{1} + (M_{2} - M_{1} )\left( {\frac{1}{2} + \frac{z}{h}} \right)^{N}$$

(85)

Therefore, each of the resultants is obtained.

Appendix 3

$$\begin{aligned} A_{1} = & \frac{{ - 12l_{1} ^{2} M2}}{{5x^{4} }} - \frac{{54{\kern 1pt} l_{0} ^{2} M2}}{{5{\kern 1pt} x^{4} }} + \frac{{ - 12{\kern 1pt} l_{0} ^{2} - 16{\kern 1pt} l_{1} ^{2} }}{{5x^{3} \tan \left( \alpha \right)}}M0 + {\kern 1pt} \frac{{4M2}}{{3x^{2} }} + \frac{{M3}}{{x^{2} }},A_{2} = \frac{{ - K0}}{x} + {\kern 1pt} \frac{{ - 4M0}}{{3x}} + \frac{{\left( {54{\kern 1pt} l_{0} ^{2} + 12{\kern 1pt} l_{1} ^{2} } \right)M0}}{{5x^{3} }}, \\ A_{3} = & {\kern 1pt} \frac{{\left( { - 54{\kern 1pt} l_{0} ^{2} - 12{\kern 1pt} l_{1} ^{2} } \right)M0}}{{5x^{4} \tan \left( \alpha \right)}} + \frac{{\left( {18{\kern 1pt} l_{0} ^{2} + 24{\kern 1pt} l_{1} ^{2} } \right)M0}}{{5x^{4} \left( {\tan \left( \alpha \right)} \right)^{3} }} + \frac{{4M0}}{{3x^{2} \tan \left( \alpha \right)}} + \frac{{K0}}{{x^{2} \tan \left( \alpha \right)}}, \\ A_{4} = & {\kern 1pt} \frac{{ - 7h}}{{3\left( {N + 1} \right)x^{4} \left( {\sin \left( \alpha \right)} \right)^{3} }}\left\{ {\left[ {x^{2} N\left( {\mu _{1} + \frac{{3k_{1} }}{7}} \right) + \frac{{ - 288{\kern 1pt} N\mu _{1} }}{{35}}\left( {l_{0} ^{2} + \frac{{7{\kern 1pt} l_{1} ^{2} }}{9} + \frac{{5{\kern 1pt} l_{2} ^{2} }}{{48}}} \right) + x^{2} \left( {\mu _{2} + \frac{{3k_{2} }}{7}} \right)} \right.} \right. \\ & \left. { + \frac{{ - 288{\kern 1pt} \mu _{2} }}{{35}}\left( {l_{0} ^{2} + \frac{{7{\kern 1pt} l_{1} ^{2} }}{9} + \frac{{5{\kern 1pt} l_{2} ^{2} }}{{48}}} \right)} \right]\cos ^{2} \left( \alpha \right) + \left( { - \mu _{1} + \frac{{ - 3k_{1} }}{7}} \right)Nx^{2} + \frac{{351{\kern 1pt} N\mu _{1} }}{{70}}\left( {l_{0} ^{2} + \frac{{88{\kern 1pt} l_{1} ^{2} }}{{351}} + \frac{{5{\kern 1pt} l_{2} ^{2} }}{{117}}} \right) \\ & \left. { + \left( { - \mu _{2} + \frac{{ - 3k_{2} }}{7}{\kern 1pt} } \right)x^{2} + \frac{{351{\kern 1pt} \mu _{2} }}{{70}}\left( {l_{0} ^{2} + \frac{{88{\kern 1pt} l_{1} ^{2} }}{{351}} + \frac{{5{\kern 1pt} l_{2} ^{2} }}{{117}}} \right)} \right\},A_{5} = \frac{{\left( { - 18{\kern 1pt} l_{0} ^{2} - 4{\kern 1pt} l_{1} ^{2} } \right)M0}}{{5x^{2} \tan \left( \alpha \right)}} \\ & + {\kern 1pt} \frac{{2\left( {27{\kern 1pt} l_{0} ^{2} + 6{\kern 1pt} l_{1} ^{2} } \right)M2}}{{5x^{3} }} + \frac{{ - M3}}{x} + \frac{{ - 4M2}}{{3x}},A_{6} = \frac{{K0}}{{x^{2} }} + {\kern 1pt} \frac{{4M0}}{{3x^{2} }} + \frac{{\left( { - 54{\kern 1pt} l_{0} ^{2} - 12{\kern 1pt} l_{1} ^{2} } \right)M0}}{{5x^{4} }} + \frac{{\left( {18{\kern 1pt} l_{0} ^{2} + 24{\kern 1pt} l_{1} ^{2} } \right)M0}}{{5x^{4} \left( {\tan \left( \alpha \right)} \right)^{2} }}, \\ A_{7} = & \frac{{ - 24{\kern 1pt} h}}{{5{\kern 1pt} x^{4} \left( {\sin \left( \alpha \right)} \right)^{3} \left( {N^{2} + 3{\kern 1pt} N + 2} \right)}}\left\{ {\frac{{ - 35{\kern 1pt} Nh\cos ^{2} \left( \alpha \right)}}{{144}}\left[ {x^{2} \left( {\mu _{1} - \mu _{2} + \frac{{3k_{1} }}{7}{\kern 1pt} + \frac{{{\kern 1pt} - 3k_{2} }}{7}} \right)} \right.} \right. \\ & \left. { - \frac{{351{\kern 1pt} \mu _{1} - 351{\kern 1pt} \mu _{2} }}{{70}}\left( {l_{0} ^{2} + \frac{{112{\kern 1pt} l_{1} ^{2} }}{{351}} + \frac{{5{\kern 1pt} l_{2} ^{2} }}{{117}}} \right)} \right] + x\sin \left( \alpha \right)\cos \left( \alpha \right)\left( {l_{0} ^{2} + \frac{{29{\kern 1pt} l_{1} ^{2} }}{{18}} + \frac{{5{\kern 1pt} l_{2} ^{2} }}{{12}}} \right)\left( {N + 2} \right)\left( {N\mu _{1} + \mu _{2} } \right) \\ & \left. { + \frac{{35{\kern 1pt} Nh}}{{144}}\left[ {x^{2} \left( {\mu _{1} - \mu _{2} + \frac{{3k_{1} }}{7} + \frac{{{\kern 1pt} - 3k_{2} }}{7}} \right) - \frac{{351{\kern 1pt} \mu _{1} - 351{\kern 1pt} \mu _{2} }}{{70}}\left( {l_{0} ^{2} + \frac{{88{\kern 1pt} l_{1} ^{2} }}{{351}} + \frac{{5{\kern 1pt} l_{2} ^{2} }}{{117}}} \right)} \right]} \right\}, \\ A_{8} = & \frac{{h\left( {N\mu _{1} + \mu _{2} } \right)}}{{x^{4} \sin ^{4} \left( \alpha \right)\left( {N + 1} \right)}}\left[ {\left( {x^{2} + \frac{{99{\kern 1pt} l_{0} ^{2} }}{{10}} + \frac{{8{\kern 1pt} l_{1} ^{2} }}{{15}} + \frac{{ - 5l_{2} ^{2} }}{2}} \right)\cos ^{2} \left( \alpha \right) - x^{2} + \frac{{ - 99{\kern 1pt} l_{0} ^{2} }}{{10}} + \frac{{ - 28{\kern 1pt} l_{1} ^{2} }}{{15}} + \frac{{{\kern 1pt} l_{2} ^{2} }}{2}} \right], \\ A_{9} = & {\kern 1pt} \frac{{M2{\kern 1pt} \left( {27{\kern 1pt} l_{0} ^{2} + 16{\kern 1pt} l_{1} ^{2} + 15{\kern 1pt} l_{2} ^{2} } \right)}}{{30x^{4} \sin ^{4} \left( \alpha \right)}},A_{{10}} = \frac{{\left( {18{\kern 1pt} l_{0} ^{2} + 4{\kern 1pt} l_{1} ^{2} } \right)M2}}{5},A_{{11}} = {\kern 1pt} \frac{{M2{\kern 1pt} \left( {27{\kern 1pt} l_{0} ^{2} + 8{\kern 1pt} l_{1} ^{2} + 3{\kern 1pt} l_{2} ^{2} } \right)}}{{6x^{2} \sin ^{2} \left( \alpha \right)}}, \\ A_{{12}} = & \frac{{2h\left( {N\mu _{1} + \mu _{2} } \right)\left( {9{\kern 1pt} l_{0} ^{2} + 2{\kern 1pt} l_{1} ^{2} } \right)}}{{5{\kern 1pt} N + 5}},A_{{13}} = \frac{{h\left( {N\mu _{1} + \mu _{2} } \right)\left( {27{\kern 1pt} l_{0} ^{2} + 16{\kern 1pt} l_{1} ^{2} + 15{\kern 1pt} l_{2} ^{2} } \right)}}{{30\left( {N + 1} \right)x^{4} \left( {\sin \left( \alpha \right)} \right)^{4} }}, \\ \end{aligned}$$

(86)

$$\begin{aligned} A_{{14}} = & - \frac{h}{{\left( {N + 1} \right)x^{3} \tan \left( \alpha \right)}}\left\{ {\left[ {\left( {k_{1} + \frac{{ - 2\mu _{1} }}{3}{\kern 1pt} } \right)x^{2} - \frac{{\left( {48{\kern 1pt} l_{0} ^{2} + 4{\kern 1pt} l_{1} ^{2} } \right)\mu _{1} }}{5}} \right]N + \left( {\frac{{ - 2\mu _{2} }}{3} + k_{2} } \right)x^{2} - \frac{{\left( {48{\kern 1pt} l_{0} ^{2} + 4{\kern 1pt} l_{1} ^{2} } \right)\mu _{2} }}{5}} \right\}, \\ A_{{15}} = & \frac{{M2{\kern 1pt} \left( {81{\kern 1pt} l_{0} ^{2} + 8{\kern 1pt} l_{1} ^{2} - 15{\kern 1pt} l_{2} ^{2} } \right)}}{{30x^{3} \left( {\sin \left( \alpha \right)} \right)^{3} }},A_{{16}} = {\kern 1pt} \frac{{M2{\kern 1pt} \left( {81{\kern 1pt} l_{0} ^{2} + 8{\kern 1pt} l_{1} ^{2} - 15{\kern 1pt} l_{2} ^{2} } \right)}}{{30x\sin \left( \alpha \right)}},A_{{17}} = {\kern 1pt} \frac{{h\left( {N\mu _{1} + \mu _{2} } \right)\left( {9{\kern 1pt} l_{0} ^{2} + 4{\kern 1pt} l_{1} ^{2} - 3{\kern 1pt} l_{2} ^{2} } \right)\cos \left( \alpha \right)}}{{3\sin ^{3} \left( \alpha \right)\left( {N + 1} \right)x^{3} }}, \\ A_{{18}} = & {\kern 1pt} \frac{{ - h\left( {N\mu _{1} + \mu _{2} } \right)\left( {441{\kern 1pt} l_{0} ^{2} + 248{\kern 1pt} l_{1} ^{2} - 15{\kern 1pt} l_{2} ^{2} } \right)\cos \left( \alpha \right)}}{{30\sin ^{3} \left( \alpha \right)\left( {N + 1} \right)x^{4} }},A_{{19}} = \frac{{ - \left( {36{\kern 1pt} l_{0} ^{2} + 8{\kern 1pt} l_{1} ^{2} } \right)\left( {N\mu _{1} + \mu _{2} } \right)h}}{{\left( {5{\kern 1pt} N + 5} \right)x^{2} \tan \left( \alpha \right)}}, \\ A_{{20}} = & \frac{{\left( {36{\kern 1pt} l_{0} ^{2} + 8{\kern 1pt} l_{1} ^{2} } \right)\left( {N\mu _{1} + \mu _{2} } \right)h}}{{\left( {5{\kern 1pt} N + 5} \right)x}},A_{{21}} = \frac{{h^{2} N\left( { - \mu _{2} + \mu _{1} } \right)\left( {351{\kern 1pt} l_{0} ^{2} + 88{\kern 1pt} l_{1} ^{2} + 15{\kern 1pt} l_{2} ^{2} } \right)}}{{60{\kern 1pt} x^{4} \left( {\sin \left( \alpha \right)} \right)^{3} \left( {N + 2} \right)\left( {N + 1} \right)}}, \\ A_{{22}} = & {\kern 1pt} \frac{{h^{2} N\left( { - \mu _{2} + \mu _{1} } \right)\left( {27{\kern 1pt} l_{0} ^{2} + 8{\kern 1pt} l_{1} ^{2} + 3{\kern 1pt} l_{2} ^{2} } \right)}}{{6x^{2} \sin \left( \alpha \right)\left( {N + 2} \right)\left( {N + 1} \right)}},A_{{23}} = \left\{ {\frac{{ - h^{2} N\left( {\cos \left( \alpha \right)} \right)^{2} }}{{6\left( {\sin \left( \alpha \right)} \right)^{3} \left( {N^{2} + 3{\kern 1pt} N + 2} \right)x^{3} }}\left[ {x^{2} \left( { - \mu _{2} + \mu _{1} + 3{\kern 1pt} k_{1} - 3{\kern 1pt} k_{2} } \right)} \right.} \right. \\ & \left. { - \frac{{ - 351{\kern 1pt} \mu _{2} + 351{\kern 1pt} \mu _{1} }}{{10}}\left( {l_{0} ^{2} + \frac{{64{\kern 1pt} l_{1} ^{2} }}{{351}} - \frac{{5{\kern 1pt} l_{2} ^{2} }}{{117}}} \right)} \right] + \frac{1}{2}x\left( {l_{0} ^{2} + \frac{{32{\kern 1pt} l_{1} ^{2} }}{9} - 5/3{\kern 1pt} l_{2} ^{2} } \right)\left( {N + 2} \right)\left( {N\mu _{1} + \mu _{2} } \right)\sin \left( {2{\kern 1pt} \alpha } \right) \\ & \left. { + \frac{5}{9}{\kern 1pt} Nh\left[ {x^{2} ( - \mu _{2} + \mu _{1} + 3{\kern 1pt} k_{1} - 3{\kern 1pt} k_{2} ) - \frac{{ - 351{\kern 1pt} \mu _{2} + 351{\kern 1pt} \mu _{1} }}{{10}}\left( {l_{0} ^{2} + \frac{{88{\kern 1pt} l_{1} ^{2} }}{{351}} + \frac{{5{\kern 1pt} l_{2} ^{2} }}{{117}}} \right)} \right]} \right\}, \\ A_{{24}} = & \frac{{ - h\left( {N\mu _{1} + \mu _{2} } \right)\left( {27{\kern 1pt} l_{0} ^{2} + 8{\kern 1pt} l_{1} ^{2} + 3{\kern 1pt} l_{2} ^{2} } \right)}}{{3\left( {N + 1} \right)x^{2} \sin \left( \alpha \right)}},A_{{25}} = \frac{{ - h\left( {N\mu _{1} + \mu _{2} } \right)\left( {351{\kern 1pt} l_{0} ^{2} + 88{\kern 1pt} l_{1} ^{2} + 15{\kern 1pt} l_{2} ^{2} } \right)}}{{30\left( {N + 1} \right)x^{4} \left( {\sin \left( \alpha \right)} \right)^{3} }}, \\ A_{{26}} = {\kern 1pt} & \frac{{h\left( {N\mu _{1} + \mu _{2} } \right)\left( {81{\kern 1pt} l_{0} ^{2} + 8{\kern 1pt} l_{1} ^{2} - 15{\kern 1pt} l_{2} ^{2} } \right)}}{{30\left( {N + 1} \right)x^{3} \left( {\sin \left( \alpha \right)} \right)^{3} }},A_{{27}} = \frac{{\left( {12{\kern 1pt} N\mu _{1} + 12{\kern 1pt} \mu _{2} } \right)\left( {l_{0} ^{2} - 1/3{\kern 1pt} l_{1} ^{2} } \right)h}}{{\left( {5{\kern 1pt} N + 5} \right)x\tan \left( \alpha \right)}}, \\ A_{{28}} = & {\kern 1pt} \frac{{ - h\left( {15{\kern 1pt} Nx^{2} k_{1} + 20{\kern 1pt} Nx^{2} \mu _{1} + 162{\kern 1pt} Nl_{0} ^{2} \mu _{1} + 36{\kern 1pt} Nl_{1} ^{2} \mu _{1} + 15{\kern 1pt} x^{2} k_{2} + 20{\kern 1pt} x^{2} \mu _{2} + 162{\kern 1pt} l_{0} ^{2} \mu _{2} + 36{\kern 1pt} l_{1} ^{2} \mu _{2} } \right)}}{{15\left( {N + 1} \right)x^{2} }}, \\ \end{aligned}$$

(87)

$$\begin{aligned} A_{{29}} = & \frac{{ - 18{\kern 1pt} h^{2} \left( {l_{0} ^{2} + 2/9{\kern 1pt} l_{1} ^{2} } \right)N\left( { - \mu _{2} + \mu _{1} } \right)}}{{5{\kern 1pt} x\left( {N + 2} \right)\left( {N + 1} \right)}},A_{{30}} = {\kern 1pt} \frac{{h\left( {N\mu _{1} + \mu _{2} } \right)\left( {81{\kern 1pt} l_{0} ^{2} + 8{\kern 1pt} l_{1} ^{2} - 15{\kern 1pt} l_{2} ^{2} } \right)}}{{30\left( {N + 1} \right)x\sin \left( \alpha \right)}},A_{{31}} = {\kern 1pt} \frac{h}{{3\left( {N + 1} \right)x^{3} \left( {\sin \left( \alpha \right)} \right)^{3} }} \\ & \left[ {\cos ^{2} \left( \alpha \right)\left[ {\left( {\left( {\mu _{1} + 3{\kern 1pt} k_{1} } \right)x^{2} + \left( { - 36{\kern 1pt} l_{0} ^{2} - 12{\kern 1pt} l_{1} ^{2} } \right)\mu _{1} } \right)N + \left( {\mu _{2} + 3{\kern 1pt} k_{2} } \right)x^{2} + \left( { - 36{\kern 1pt} l_{0} ^{2} - 12{\kern 1pt} l_{1} ^{2} } \right)\mu _{2} } \right] + N[\left( { - \mu _{1} - 3{\kern 1pt} k_{1} } \right)x^{2} } \right. \\ & \left. {\left. { + \frac{{351{\kern 1pt} \mu _{1} }}{{10}}\left( {l_{0} ^{2} + \frac{{88{\kern 1pt} l_{1} ^{2} }}{{351}} + \frac{{5{\kern 1pt} l_{2} ^{2} }}{{117}}} \right)} \right] + \left( { - \mu _{2} - 3{\kern 1pt} k_{2} } \right)x^{2} + \frac{{351{\kern 1pt} \mu _{2} }}{{10}}\left( {l_{0} ^{2} + \frac{{88{\kern 1pt} l_{1} ^{2} }}{{351}} + \frac{{5{\kern 1pt} l_{2} ^{2} }}{{117}}} \right)} \right], \\ A_{{32}} = & {\kern 1pt} \frac{{h\left( {N\mu _{1} + \mu _{2} } \right)\left( {27{\kern 1pt} l_{0} ^{2} + 8{\kern 1pt} l_{1} ^{2} + 3{\kern 1pt} l_{2} ^{2} } \right)}}{{6\left( {N + 1} \right)x^{2} \left( {\sin \left( \alpha \right)} \right)^{2} }},A_{{33}} = {\kern 1pt} \frac{{ - h\left( {N\mu _{1} + \mu _{2} } \right)\left( {27{\kern 1pt} l_{0} ^{2} + 8{\kern 1pt} l_{1} ^{2} + 3{\kern 1pt} l_{2} ^{2} } \right)}}{{6\left( {N + 1} \right)x^{3} \left( {\sin \left( \alpha \right)} \right)^{2} }}, \\ A_{{34}} = & \frac{{h^{2} N\left( { - \mu _{2} + \mu _{1} } \right)\left( {27{\kern 1pt} l_{0} ^{2} + 8{\kern 1pt} l_{1} ^{2} + 3{\kern 1pt} l_{2} ^{2} } \right)}}{{12x^{3} \left( {\sin \left( \alpha \right)} \right)^{2} \left( {N + 2} \right)\left( {N + 1} \right)}},A_{{35}} = {\kern 1pt} \frac{{6h}}{{5x^{2} \left( {N + 2} \right)\left( {N + 1} \right)\tan \left( \alpha \right)}}\left\{ {\frac{{ - 5Nh\tan \left( \alpha \right)}}{9}} \right. \\ & \left. {\left[ {\left( {\mu _{2} - \frac{3}{4}{\kern 1pt} k_{1} + \frac{3}{4}{\kern 1pt} k_{2} - \mu _{1} } \right)x^{2} + \frac{{\left( {81{\kern 1pt} \mu _{2} - 81{\kern 1pt} \mu _{1} } \right)\left( {l_{0} ^{2} + 2/9{\kern 1pt} l_{1} ^{2} } \right)}}{{10}}} \right] + \left( {N + 2} \right)\left( {l_{0} ^{2} - 1/3{\kern 1pt} l_{1} ^{2} } \right)\left( {N\mu _{1} + \mu _{2} } \right)x} \right\}, \\ A_{{36}} = & \frac{{9{\kern 1pt} h}}{{10{\kern 1pt} \left( {\sin \left( \alpha \right)} \right)^{4} x^{4} \left( {N + 2} \right)\left( {N + 1} \right)}}\left\{ {\frac{{\left( {5{\kern 1pt} \mu _{2} - 5{\kern 1pt} \mu _{1} } \right)Nh\cos ^{2} \left( \alpha \right)}}{9}{\kern 1pt} \left[ {x^{2} + \frac{{99{\kern 1pt} l_{0} ^{2} }}{{10}} + \frac{{28{\kern 1pt} l_{1} ^{2} }}{{15}} - \frac{{3{\kern 1pt} l_{2} ^{2} }}{2}} \right]} \right. \\ & \left. { + \frac{{x\left( {N\mu _{1} + \mu _{2} } \right)\sin \left( {2{\kern 1pt} \alpha } \right)\left( {N + 2} \right)}}{2}{\kern 1pt} \left( {l_{0} ^{2} + \frac{{56{\kern 1pt} l_{1} ^{2} }}{{27}} + \frac{{25{\kern 1pt} l_{2} ^{2} }}{9}} \right) + \frac{{ - 5\left( {\mu _{2} - \mu _{1} } \right)Nh}}{9}{\kern 1pt} \left( {x^{2} + \frac{{99{\kern 1pt} l_{0} ^{2} }}{{10}} + \frac{{28{\kern 1pt} l_{1} ^{2} }}{{15}} - \frac{{l_{2} ^{2} }}{2}} \right)} \right\} \\ & ,I_{0} = \rho _{1} h + \frac{{h\left( {\rho _{2} - \rho _{1} } \right)}}{{N + 1}},I_{1} = \frac{{h^{2} N\left( {\rho _{2} - \rho _{1} } \right)}}{{2{\kern 1pt} N^{2} + 6{\kern 1pt} N + 4}},f_{{E1}} = (f_{1}^{E} )_{1} + \left[ {(f_{1}^{E} )_{2} - (f_{1}^{E} )_{1} } \right]\left( {\frac{1}{2} + \frac{z}{h}} \right)^{N} , \\ f_{{E2}} = & (f_{2}^{E} )_{1} + \left[ {(f_{2}^{E} )_{2} - (f_{2}^{E} )_{1} } \right]\left( {\frac{1}{2} + \frac{z}{h}} \right)^{N} ,f_{{M1}} = (f_{1}^{M} )_{1} + \left[ {(f_{1}^{M} )_{2} - (f_{1}^{M} )_{1} } \right]\left( {\frac{1}{2} + \frac{z}{h}} \right)^{N} , \\ f_{{M2}} = & (f_{2}^{M} )_{1} + [(f_{2}^{M} )_{2} - (f_{2}^{M} )_{1} ]\left( {\frac{1}{2} + \frac{z}{h}} \right)^{N} . \\ \end{aligned}$$

(88)

$$\begin{aligned} B_{1} = & \frac{{h^{2} \left( {\mu _{2} - \mu _{1} } \right)N\left( {81{\kern 1pt} l_{0} ^{2} + 8{\kern 1pt} l_{1} ^{2} - 15{\kern 1pt} l_{2} ^{2} } \right)}}{{60{\kern 1pt} x\left( {N + 2} \right)\left( {N + 1} \right)\sin \left( \alpha \right)}},B_{2} = {\kern 1pt} \frac{{h^{2} \left( {\mu _{2} - \mu _{1} } \right)N\left( {27{\kern 1pt} l_{0} ^{2} + 8{\kern 1pt} l_{1} ^{2} + 3{\kern 1pt} l_{2} ^{2} } \right)}}{{6x^{2} \sin \left( \alpha \right)\left( {N + 2} \right)\left( {N + 1} \right)}}, \\ B_{3} = & {\kern 1pt} \frac{{h^{2} \left( {\mu _{2} - \mu _{1} } \right)N\left( {63{\kern 1pt} l_{0} ^{2} + 24{\kern 1pt} l_{1} ^{2} + 15{\kern 1pt} l_{2} ^{2} } \right)}}{{20x^{4} \left( {\sin \left( \alpha \right)} \right)^{3} \left( {N + 2} \right)\left( {N + 1} \right)}},B_{6} = \frac{{9h^{2} \left( {\mu _{2} - \mu _{1} } \right)N\left( {l_{0} ^{2} + 2/9{\kern 1pt} l_{1} ^{2} } \right)}}{{5x^{4} \left( {\sin \left( \alpha \right)} \right)^{4} \left( {N + 2} \right)\left( {N + 1} \right)}}, \\ B_{5} = & {\kern 1pt} \frac{{h^{2} \left( {\mu _{2} - \mu _{1} } \right)N\left( {27{\kern 1pt} l_{0} ^{2} + 8{\kern 1pt} l_{1} ^{2} + 3{\kern 1pt} l_{2} ^{2} } \right)}}{{12x^{2} \left( {\sin \left( \alpha \right)} \right)^{2} \left( {N + 2} \right)\left( {N + 1} \right)}},B_{4} = \frac{{h^{2} \left( {\mu _{2} - \mu _{1} } \right)N\left( {81{\kern 1pt} l_{0} ^{2} + 8{\kern 1pt} l_{1} ^{2} - 15{\kern 1pt} l_{2} ^{2} } \right)}}{{60{\kern 1pt} x^{3} \left( {\sin \left( \alpha \right)} \right)^{3} \left( {N + 2} \right)\left( {N + 1} \right)}}, \\ B_{7} = & {\kern 1pt} \frac{{h^{2} \left( { - \mu _{2} + \mu _{1} } \right)N\left( {27{\kern 1pt} l_{0} ^{2} + 8{\kern 1pt} l_{1} ^{2} + 3{\kern 1pt} l_{2} ^{2} } \right)}}{{12x^{3} \left( {\sin \left( \alpha \right)} \right)^{2} \left( {N + 2} \right)\left( {N + 1} \right)}},B_{8} = \frac{{h\left( {N\mu _{1} + \mu _{2} } \right)\left( {18{\kern 1pt} l_{0} ^{2} + 4{\kern 1pt} l_{1} ^{2} } \right)}}{{5\left( {N + 1} \right)x^{4} \left( {\sin \left( \alpha \right)} \right)^{4} }}, \\ B_{9} = & \frac{{9{\kern 1pt} h}}{{10{\kern 1pt} x^{2} \left( {\sin \left( \alpha \right)} \right)^{2} \left( {N + 2} \right)\left( {N + 1} \right)}}\left[ {\frac{{5h\left( {\mu _{2} - \mu _{1} } \right)N\cos ^{2} \left( \alpha \right)\left( {x^{2} + 9/5{\kern 1pt} l_{0} ^{2} + \frac{{32{\kern 1pt} l_{1} ^{2} }}{{15}} + l_{2} ^{2} } \right)}}{9}} \right. \\ {\kern 1pt} & \left. { + \frac{{x\sin (2{\kern 1pt} \alpha )\left( {N\mu _{1} + \mu _{2} } \right)\left( {N + 2} \right)\left( {\frac{{ - 5l_{2} ^{2} }}{3}{\kern 1pt} + l_{0} ^{2} + \frac{{4l_{1} ^{2} }}{3}} \right)}}{2} + {\kern 1pt} \frac{{ - 5h\left( {\mu _{2} - \mu _{1} } \right)\left( {x^{2} + \frac{{27{\kern 1pt} l_{0} ^{2} }}{{10}} + \frac{{8{\kern 1pt} l_{1} ^{2} }}{5} + \frac{{3{\kern 1pt} l_{2} ^{2} }}{2}} \right)N}}{9}} \right], \\ B_{{10}} = & \frac{{h\left( {N\mu _{1} + \mu _{2} } \right)\left( {27{\kern 1pt} l_{0} ^{2} + 8{\kern 1pt} l_{1} ^{2} + 3{\kern 1pt} l_{2} ^{2} } \right)}}{{3\left( {N + 1} \right)x^{2} \sin \left( \alpha \right)}},B_{{11}} = \frac{{h\left( {N\mu _{1} + \mu _{2} } \right)\left( {27{\kern 1pt} l_{0} ^{2} + 8{\kern 1pt} l_{1} ^{2} + 3{\kern 1pt} l_{2} ^{2} } \right)}}{{6\left( {N + 1} \right)x^{2} \left( {\sin \left( \alpha \right)} \right)^{2} }}, \\ B_{{12}} = & \frac{{h\left( {N\mu _{1} + \mu _{2} } \right)}}{{\left( {N + 1} \right)x^{2} \left( {\sin \left( \alpha \right)} \right)^{2} }}\left[ {\left( {x^{2} + \frac{{9{\kern 1pt} l_{0} ^{2} }}{{10}} + \frac{{8{\kern 1pt} l_{1} ^{2} }}{{15}} + \frac{{l_{2} ^{2} }}{2}} \right)\cos ^{2} \left( \alpha \right) - x^{2} + \frac{{ - 27{\kern 1pt} l_{0} ^{2} }}{{10}} + \frac{{ - 8{\kern 1pt} l_{1} ^{2} }}{5} + \frac{{ - 3l_{2} ^{2} }}{2}} \right], \\ B_{{13}} = & \frac{{h\left( {N\mu _{1} + \mu _{2} } \right)\left( {81{\kern 1pt} l_{0} ^{2} + 8{\kern 1pt} l_{1} ^{2} - 15{\kern 1pt} l_{2} ^{2} } \right)}}{{30\left( {N + 1} \right)x\sin \left( \alpha \right)}}, \\ \end{aligned}$$

(89)

$$\begin{gathered} B_{{14}} = \frac{{ - Nh^{2} \left( {\cos \left( \alpha \right)} \right)^{2} \left( {\left( { - \mu _{2} + \mu _{1} + 3{\kern 1pt} k_{1} - 3{\kern 1pt} k_{2} } \right)x^{2} + 18{\kern 1pt} \left( { - \mu _{2} + \mu _{1} } \right)\left( {l_{0} ^{2} + 4/9{\kern 1pt} l_{1} ^{2} + 1/3{\kern 1pt} l_{2} ^{2} } \right)} \right)}}{{6x^{3} \left( {\sin \left( \alpha \right)} \right)^{3} \left( {N + 2} \right)\left( {N + 1} \right)}} \hfill \\ + \frac{{3h\left( {l_{0} ^{2} + 4/9{\kern 1pt} l_{1} ^{2} - 1/3{\kern 1pt} l_{2} ^{2} } \right)\left( {N\mu _{1} + \mu _{2} } \right)\sin \left( {2{\kern 1pt} \alpha } \right)}}{{2x^{2} \left( {\sin \left( \alpha \right)} \right)^{3} \left( {N + 1} \right)}} + {\kern 1pt} \frac{{Nh^{2} }}{{6x^{3} \left( {\sin \left( \alpha \right)} \right)^{3} \left( {N + 2} \right)\left( {N + 1} \right)}}[\left( { - \mu _{2} + \mu _{1} + 3{\kern 1pt} k_{1} - 3{\kern 1pt} k_{2} } \right)x^{2} \hfill \\ + (\frac{{ - 189{\kern 1pt} \mu _{2} }}{{10}} + \frac{{189{\kern 1pt} \mu _{1} }}{{10}})(l_{0} ^{2} + \frac{{8{\kern 1pt} l_{1} ^{2} }}{{21}} + \frac{{5{\kern 1pt} l_{2} ^{2} }}{{21}})],B_{{15}} = \frac{{39{\kern 1pt} h}}{{10{\kern 1pt} x^{4} \left( {\sin \left( \alpha \right)} \right)^{4} \left( {N + 2} \right)\left( {N + 1} \right)}}\{ \hfill \\ - \frac{{20{\kern 1pt} h\left( {\cos \left( \alpha \right)} \right)^{2} N}}{{117}}[(\mu _{1} - \mu _{2} + \frac{{3{\kern 1pt} k_{1} }}{4} + \frac{{ - 3{\kern 1pt} k_{2} }}{4})x^{2} + \frac{{63{\kern 1pt} \mu _{2} - 63{\kern 1pt} \mu _{1} }}{{40}}(l_{0} ^{2} + \frac{{16{\kern 1pt} l_{1} ^{2} }}{{21}} + \frac{{ - 5{\kern 1pt} l_{2} ^{2} }}{7})] \hfill \\ + {\kern 1pt} \frac{{\left( {N\mu _{1} + \mu _{2} } \right)\sin \left( {2{\kern 1pt} \alpha } \right)\left( {N + 2} \right)x}}{2}(l_{0} ^{2} + \frac{{176{\kern 1pt} l_{1} ^{2} }}{{117}} - \frac{{5{\kern 1pt} l_{2} ^{2} }}{{39}}) + \frac{{20{\kern 1pt} hN}}{{117}}[(\mu _{1} - \mu _{2} + \frac{{3{\kern 1pt} k_{1} }}{4} + \frac{{ - 3{\kern 1pt} k_{2} }}{4})x^{2} \hfill \\ + \frac{{27{\kern 1pt} \mu _{2} - 27{\kern 1pt} \mu _{1} }}{{40}}(l_{0} ^{2} + \frac{{ - 8{\kern 1pt} l_{1} ^{2} }}{9} + \frac{{ - 5{\kern 1pt} l_{2} ^{2} }}{3})]\} ,B_{{16}} = \frac{{ - h\left( {N\mu _{1} + \mu _{2} } \right)\left( {27{\kern 1pt} l_{0} ^{2} + 8{\kern 1pt} l_{1} ^{2} + 3{\kern 1pt} l_{2} ^{2} } \right)}}{{6\left( {N + 1} \right)x^{3} \left( {\sin \left( \alpha \right)} \right)^{2} }}, \hfill \\ B_{{17}} = \frac{{h\left( {N\mu _{1} + \mu _{2} } \right)\left( {81{\kern 1pt} l_{0} ^{2} + 8{\kern 1pt} l_{1} ^{2} - 15{\kern 1pt} l_{2} ^{2} } \right)}}{{30\left( {N + 1} \right)x^{3} \left( {\sin \left( \alpha \right)} \right)^{3} }}, \hfill \\ B_{{18}} = \frac{{h\left( {N\mu _{1} + \mu _{2} } \right)}}{{\left( {N + 1} \right)x^{3} \sin ^{2} \left( \alpha \right)}}[(x^{2} + \frac{{ - 9{\kern 1pt} l_{0} ^{2} }}{{10}} + \frac{{ - 8{\kern 1pt} l_{1} ^{2} }}{{15}} + \frac{{ - {\kern 1pt} l_{2} ^{2} }}{2})\cos ^{2} \left( \alpha \right) - x^{2} + \frac{{27{\kern 1pt} l_{0} ^{2} }}{{10}} + \frac{{8l_{1} ^{2} }}{5} + \frac{{3{\kern 1pt} l_{2} ^{2} }}{2}], \hfill \\ \end{gathered}$$

(90)

$$\begin{aligned} B_{{19}} = & {\kern 1pt} \frac{{9h}}{{2x^{4} \left( {\sin \left( \alpha \right)} \right)^{3} \left( {N + 2} \right)\left( {N + 1} \right)}}\left\{ { - \frac{{7{\kern 1pt} hN\left( {\cos \left( \alpha \right)} \right)^{2} }}{{27}}} \right.\left[ {x^{2} \left( {\mu _{1} - \mu _{2} + \frac{{3k_{1} }}{7} + \frac{{ - 3{\kern 1pt} k_{2} }}{7}} \right) + \frac{{18{\kern 1pt} \mu _{2} - 18{\kern 1pt} \mu _{1} }}{5}\left( {l_{0} ^{2} + \frac{{44{\kern 1pt} l_{1} ^{2} }}{{63}} + \frac{{5{\kern 1pt} l_{2} ^{2} }}{{14}}} \right)} \right] \\ & \left. { + \frac{{x\left( {N\mu _{1} + \mu _{2} } \right)\sin \left( {2{\kern 1pt} \alpha } \right)\left( {N + 2} \right)}}{2}\left( {l_{0} ^{2} + \frac{{40{\kern 1pt} l_{1} ^{2} }}{{27}} + \frac{{5{\kern 1pt} l_{2} ^{2} }}{9}} \right) + \frac{{7{\kern 1pt} hN}}{{27}}\left[ {x^{2} \left( {\mu _{1} - \mu _{2} + \frac{{3k_{1} }}{7} + \frac{{ - 3{\kern 1pt} k_{2} }}{7}} \right) + \frac{{27{\kern 1pt} \mu _{2} - 27{\kern 1pt} \mu _{1} }}{{10}}\left( {l_{0} ^{2} + \frac{{8{\kern 1pt} l_{1} ^{2} }}{{21}} + \frac{{5{\kern 1pt} l_{2} ^{2} }}{{21}}} \right)} \right]} \right\}, \\ B_{{20}} = & \frac{{h\left( {N\mu _{1} + \mu _{2} } \right)}}{{30\left( {N + 1} \right)x^{4} \left( {\sin \left( \alpha \right)} \right)^{4} }}\left[ {80{\kern 1pt} \left( {\cos \left( \alpha \right)} \right)^{4} l_{1} ^{2} - 60{\kern 1pt} \left( {\cos \left( \alpha \right)} \right)^{4} l_{2} ^{2} - 30{\kern 1pt} \left( {\cos \left( \alpha \right)} \right)^{2} x^{2} + 108{\kern 1pt} \left( {\cos \left( \alpha \right)} \right)^{2} l_{0} ^{2} + 104{\kern 1pt} \left( {\cos \left( \alpha \right)} \right)^{2} l_{1} ^{2} } \right. \\ & \left. { + 120{\kern 1pt} \left( {\cos \left( \alpha \right)} \right)^{2} l_{2} ^{2} + 30{\kern 1pt} x^{2} - 81{\kern 1pt} l_{0} ^{2} - 48{\kern 1pt} l_{1} ^{2} - 45{\kern 1pt} l_{2} ^{2} } \right], \\ B_{{21}} = & \frac{h}{{\left( {\sin \left( \alpha \right)} \right)^{4} x^{4} \left( {N + 2} \right)\left( {N + 1} \right)}}\left\{ {\frac{{ - N\left( { - \mu _{2} + \mu _{1} } \right)h\left( {\cos \left( \alpha \right)} \right)^{4} }}{2}\left( {x^{2} - \frac{{18{\kern 1pt} l_{0} ^{2} }}{5} - \frac{{16{\kern 1pt} l_{1} ^{2} }}{{15}}} \right)} \right. \\ & + x\sin \left( \alpha \right)\cos ^{3} \left( \alpha \right)\left( {N\mu _{1} + \mu _{2} } \right)\left( {N + 2} \right)\left( {x^{2} - \frac{{9{\kern 1pt} l_{0} ^{2} }}{{10}} - \frac{{16{\kern 1pt} l_{1} ^{2} }}{5} + \frac{{3{\kern 1pt} l_{2} ^{2} }}{2}} \right) + N\left( { - \mu _{2} + \mu _{1} } \right)h\left( {\cos \left( \alpha \right)} \right)^{2} \left( {x^{2} + \frac{{ - 63{\kern 1pt} l_{0} ^{2} }}{{20}} + \frac{{ - 32{\kern 1pt} l_{1} ^{2} }}{{15}} + \frac{{ - 3{\kern 1pt} l_{2} ^{2} }}{4}} \right) \\ & \left. { + \frac{{ - \sin \left( {2{\kern 1pt} \alpha } \right)\left( {N\mu _{1} + \mu _{2} } \right)\left( {N + 2} \right)x}}{2}\left( {x^{2} + \frac{{4{\kern 1pt} l_{1} ^{2} }}{3} + 2{\kern 1pt} l_{2} ^{2} } \right) + \frac{{ - N\left( { - \mu _{2} + \mu _{1} } \right)h}}{2}\left( {x^{2} + \frac{{ - 27{\kern 1pt} l_{0} ^{2} }}{{10}} + \frac{{ - 8{\kern 1pt} l_{1} ^{2} }}{5} + \frac{{ - 3{\kern 1pt} l_{2} ^{2} }}{2}} \right)} \right\}, \\ B_{{22}} = & \frac{{ - 9{\kern 1pt} h}}{{10{\kern 1pt} x^{3} \sin ^{2} \left( \alpha \right)\left( {N + 2} \right)\left( {N + 1} \right)}}\left[ {\frac{{5hN\left( { - \mu _{2} + \mu _{1} } \right)\cos ^{2} \left( \alpha \right)}}{9}\left( {x^{2} + \frac{{ - 18{\kern 1pt} l_{0} ^{2} }}{5} + \frac{{ - 8{\kern 1pt} l_{1} ^{2} }}{3} + l_{2} ^{2} } \right)} \right. \\ & \left. { + {\kern 1pt} \frac{{\sin \left( {2{\kern 1pt} \alpha } \right)\left( {N\mu _{1} + \mu _{2} } \right)\left( {N + 2} \right)x}}{2}\left( {l_{0} ^{2} + \frac{{16{\kern 1pt} l_{1} ^{2} }}{{27}} + 5/9{\kern 1pt} l_{2} ^{2} } \right) + \frac{{ - 5N\left( { - \mu _{2} + \mu _{1} } \right)h}}{9}\left( {x^{2} + \frac{{ - 27{\kern 1pt} l_{0} ^{2} }}{{10}} + \frac{{ - 8{\kern 1pt} l_{1} ^{2} }}{5} + \frac{{ - 3{\kern 1pt} l_{2} ^{2} }}{2}} \right)} \right], \\ \end{aligned}$$

(91)

$$\begin{aligned} B_{{23}} = {\kern 1pt} & \frac{{7h\cos \left( \alpha \right)}}{{3\left( {N + 1} \right)x^{4} \left( {\sin \left( \alpha \right)} \right)^{4} }}\left\{ {x^{2} N\cos ^{2} \left( \alpha \right)\left( {\mu _{1} + \frac{{3{\kern 1pt} k_{1} }}{7}} \right) + \frac{{ - 198{\kern 1pt} N\mu _{1} \cos ^{2} \left( \alpha \right)}}{{35}}\left( {l_{0} ^{2} + \frac{{112{\kern 1pt} l_{1} ^{2} }}{{99}} + \frac{{5{\kern 1pt} l_{2} ^{2} }}{{33}}} \right) + x^{2} \cos ^{2} \left( \alpha \right)\left( {\mu _{2} + \frac{{3k_{2} }}{7}} \right)} \right. \\ & + \frac{{ - 198{\kern 1pt} \mu _{2} \cos ^{2} \left( \alpha \right)}}{{35}}\left( {l_{0} ^{2} + \frac{{112{\kern 1pt} l_{1} ^{2} }}{{99}} + \frac{{5{\kern 1pt} l_{2} ^{2} }}{{33}}} \right) + x^{2} N\left( { - \mu _{1} + \frac{{ - 3{\kern 1pt} k_{1} }}{7}} \right) + \frac{{\mu _{1} N}}{{10}}\left( {27{\kern 1pt} l_{0} ^{2} + \frac{{72{\kern 1pt} l_{1} ^{2} }}{7} + \frac{{45{\kern 1pt} l_{2} ^{2} }}{7}} \right) + x^{2} \left( { - \mu _{2} + \frac{{ - 3{\kern 1pt} k_{2} }}{7}} \right) \\ & \left. { + \frac{{\mu _{2} }}{{10}}\left( {27{\kern 1pt} l_{0} ^{2} + \frac{{72{\kern 1pt} l_{1} ^{2} }}{7} + \frac{{45{\kern 1pt} l_{2} ^{2} }}{7}} \right)} \right\},B_{{24}} = \frac{{7h}}{{3\left( {N + 1} \right)x^{4} \sin ^{3} \left( \alpha \right)}}\left\{ {x^{2} N\cos ^{2} \left( \alpha \right)\left( {\mu _{1} + \frac{{3{\kern 1pt} k_{1} }}{7}} \right)} \right. \\ & + \frac{{ - 198{\kern 1pt} N\mu _{1} \cos ^{2} \left( \alpha \right)}}{{35}}\left( {l_{0} ^{2} + \frac{{92{\kern 1pt} l_{1} ^{2} }}{{99}} + \frac{{10{\kern 1pt} l_{2} ^{2} }}{{33}}} \right) + x^{2} \cos ^{2} \left( \alpha \right)\left( {\mu _{2} + \frac{{3k_{2} }}{7}} \right) + \frac{{ - 198{\kern 1pt} \mu _{2} \cos ^{2} \left( \alpha \right)}}{{35}}\left( {l_{0} ^{2} + \frac{{92{\kern 1pt} l_{1} ^{2} }}{{99}} + \frac{{10{\kern 1pt} l_{2} ^{2} }}{{33}}} \right) \\ & \left. { + x^{2} N\left( { - \mu _{1} + \frac{{ - 3{\kern 1pt} k_{1} }}{7}} \right) + \frac{{\mu _{1} N}}{{10}}\left( {27{\kern 1pt} l_{0} ^{2} + \frac{{72{\kern 1pt} l_{1} ^{2} }}{7} + \frac{{45{\kern 1pt} l_{2} ^{2} }}{7}} \right) + x^{2} \left( { - \mu _{2} + \frac{{ - 3{\kern 1pt} k_{2} }}{7}} \right) + \frac{{\mu _{2} }}{{10}}\left( {27{\kern 1pt} l_{0} ^{2} + \frac{{72{\kern 1pt} l_{1} ^{2} }}{7} + \frac{{45{\kern 1pt} l_{2} ^{2} }}{7}} \right)} \right\}, \\ B_{{25}} = & \frac{h}{{3\left( {N + 1} \right)x^{3} \left( {\sin \left( \alpha \right)} \right)^{3} }}\left\{ {x^{2} N\cos ^{2} \left( \alpha \right)\left( {\mu _{1} + 3{\kern 1pt} k_{1} } \right) + 18N\cos ^{2} \left( \alpha \right){\kern 1pt} \left( {l_{0} ^{2} + \frac{{2{\kern 1pt} l_{1} ^{2} }}{9} + \frac{{{\kern 1pt} l_{2} ^{2} }}{3}} \right)\mu _{1} + x^{2} \cos ^{2} \left( \alpha \right){\kern 1pt} \left( {\mu _{2} + 3{\kern 1pt} k_{2} } \right)} \right. \\ & + 18{\kern 1pt} \cos ^{2} \left( \alpha \right){\kern 1pt} \left( {l_{0} ^{2} + \frac{{2{\kern 1pt} l_{1} ^{2} }}{9} + \frac{{{\kern 1pt} l_{2} ^{2} }}{3}} \right)\mu _{2} + \left( { - \mu _{1} - 3{\kern 1pt} k_{1} } \right)x^{2} N + \frac{{ - 189{\kern 1pt} N\mu _{1} }}{{10}}\left( {l_{0} ^{2} + \frac{{8{\kern 1pt} l_{1} ^{2} }}{{21}} + \frac{{5{\kern 1pt} l_{2} ^{2} }}{{21}}} \right) + \left( { - \mu _{2} - 3{\kern 1pt} k_{2} } \right)x^{2} \\ & \left. { + \frac{{ - 189{\kern 1pt} \mu _{2} }}{{10}}\left( {l_{0} ^{2} + \frac{{8{\kern 1pt} l_{1} ^{2} }}{{21}} + \frac{{5{\kern 1pt} l_{2} ^{2} }}{{21}}} \right)} \right\},B_{{26}} = \frac{{h\left( {N\mu _{1} + \mu _{2} } \right)\left( {27{\kern 1pt} l_{0} ^{2} + 16{\kern 1pt} l_{1} ^{2} + 15{\kern 1pt} l_{2} ^{2} } \right)}}{{15\left( {N + 1} \right)x}}, \\ \end{aligned}$$

(92)

$$\begin{aligned} B_{{27}} = & \frac{{4h}}{{3\left( {N + 1} \right)x^{4} \left( {\sin \left( \alpha \right)} \right)^{4} }}\left\{ {x^{2} N\cos ^{2} \left( \alpha \right)\left( {\mu _{1} + \frac{{3{\kern 1pt} k_{1} }}{4}} \right) - \frac{{153{\kern 1pt} N\mu _{1} \left( {\cos \left( \alpha \right)} \right)^{2} }}{{20}}\left( {l_{0} ^{2} + \frac{{164{\kern 1pt} l_{1} ^{2} }}{{153}} - \frac{{5{\kern 1pt} l_{2} ^{2} }}{{51}}} \right) + x^{2} \cos ^{2} \left( \alpha \right)\left( {\mu _{2} + \frac{{3{\kern 1pt} k_{2} }}{4}} \right)} \right. \\ & - \frac{{153{\kern 1pt} \mu _{2} \left( {\cos \left( \alpha \right)} \right)^{2} }}{{20}}\left( {l_{0} ^{2} + \frac{{164{\kern 1pt} l_{1} ^{2} }}{{153}} - \frac{{5{\kern 1pt} l_{2} ^{2} }}{{51}}} \right) + x^{2} N\left( { - \mu _{1} + \frac{{ - 3{\kern 1pt} k_{1} }}{4}} \right) + \mu _{1} N\left( {\frac{{27{\kern 1pt} l_{0} ^{2} }}{{40}} + \frac{{ - 24{\kern 1pt} l_{1} ^{2} }}{{40}} + \frac{{ - 45{\kern 1pt} l_{2} ^{2} }}{{40}}} \right) + \left( { - \mu _{2} + \frac{{ - 3{\kern 1pt} k_{2} }}{4}} \right)x^{2} \\ & \left. { + \mu _{2} \left( {\frac{{27{\kern 1pt} l_{0} ^{2} }}{{40}} + \frac{{ - 24{\kern 1pt} l_{1} ^{2} }}{{40}} + \frac{{ - 45{\kern 1pt} l_{2} ^{2} }}{{40}}} \right)} \right\},B_{{28}} = \frac{{h\left( {N\mu _{1} + \mu _{2} } \right)\left( {27{\kern 1pt} l_{0} ^{2} + 16{\kern 1pt} l_{1} ^{2} + 15{\kern 1pt} l_{2} ^{2} } \right)}}{{30{\kern 1pt} N + 30}}, \\ B_{{29}} = & \frac{{h\cos \left( \alpha \right)\left( {N\mu _{1} + \mu _{2} } \right)\left( {207{\kern 1pt} l_{0} ^{2} + 136{\kern 1pt} l_{1} ^{2} + 15{\kern 1pt} l_{2} ^{2} } \right)}}{{30\left( {N + 1} \right)x^{4} \left( {\sin \left( \alpha \right)} \right)^{4} }},B_{{30}} = \frac{{h^{2} \left( {\mu _{2} - \mu _{1} } \right)N\left( {27{\kern 1pt} l_{0} ^{2} + 16{\kern 1pt} l_{1} ^{2} + 15{\kern 1pt} l_{2} ^{2} } \right)}}{{30x\left( {N + 2} \right)\left( {N + 1} \right)}}, \\ B_{{31}} = & \frac{{ - 2h\left( {N\mu _{1} + \mu _{2} } \right)\left( {9{\kern 1pt} l_{0} ^{2} + 2{\kern 1pt} l_{1} ^{2} + 3{\kern 1pt} l_{2} ^{2} } \right)\cos \left( \alpha \right)}}{{3\left( {\sin \left( \alpha \right)} \right)^{2} \left( {N + 1} \right)x^{3} }},B_{{32}} = \frac{{h\left( {N\mu _{1} + \mu _{2} } \right)\left( {63{\kern 1pt} l_{0} ^{2} + 24{\kern 1pt} l_{1} ^{2} + 15{\kern 1pt} l_{2} ^{2} } \right)\cos \left( \alpha \right)}}{{10\left( {\sin \left( \alpha \right)} \right)^{2} \left( {N + 1} \right)x^{2} }}, \\ B_{{33}} = & \frac{{h^{2} \left( {\mu _{2} - \mu _{1} } \right)N\left( {27{\kern 1pt} l_{0} ^{2} + 16{\kern 1pt} l_{1} ^{2} + 15{\kern 1pt} l_{2} ^{2} } \right)}}{{\left( {60{\kern 1pt} N + 120} \right)\left( {N + 1} \right)}},B_{{34}} = {\kern 1pt} \frac{{h\left( {N\mu _{1} + \mu _{2} } \right)\left( {63{\kern 1pt} l_{0} ^{2} + 24{\kern 1pt} l_{1} ^{2} + 15{\kern 1pt} l_{2} ^{2} } \right)}}{{10\left( {N + 1} \right)x^{4} \left( {\sin \left( \alpha \right)} \right)^{3} }}, \\ \end{aligned}$$

(93)

$$\begin{aligned} C_{1} = & \frac{{h\left( {N\mu _{1} + \mu _{2} } \right)\left( {30{\kern 1pt} \left( {\cos \left( \alpha \right)} \right)^{2} x^{2} - 12{\kern 1pt} \left( {\cos \left( \alpha \right)} \right)^{2} l_{0} ^{2} + 24{\kern 1pt} \left( {\cos \left( \alpha \right)} \right)^{2} l_{1} ^{2} - 30{\kern 1pt} x^{2} + 27{\kern 1pt} l_{0} ^{2} + 16{\kern 1pt} l_{1} ^{2} + 15{\kern 1pt} l_{2} ^{2} } \right)}}{{30\left( {N + 1} \right)x^{3} \left( {\sin \left( \alpha \right)} \right)^{2} }}, \\ C_{2} = & \frac{h}{{x^{4} \left( {\sin \left( \alpha \right)} \right)^{4} \left( {N + 2} \right)\left( {N + 1} \right)}}\left\{ {\frac{{2{\kern 1pt} hx^{2} N\cos ^{3} \left( \alpha \right)}}{3}\left( {\mu _{1} - \mu _{2} + \frac{{3k_{1} }}{4} + \frac{{ - 3{\kern 1pt} k_{2} }}{4}} \right)} \right. \\ & + \frac{{11hN\cos ^{3} \left( \alpha \right)\left( { - \mu _{2} + \mu _{1} } \right)}}{4}\left( {l_{0} ^{2} - \frac{{32{\kern 1pt} l_{1} ^{2} }}{{165}} + \frac{{ - {\kern 1pt} l_{2} ^{2} }}{{11}}} \right) + \frac{{{\kern 1pt} \left( {N + 2} \right)\left( {N\mu _{1} + \mu _{2} } \right)x\sin \left( {2{\kern 1pt} \alpha } \right)\cos \left( \alpha \right)}}{2}\left( { - \frac{{24{\kern 1pt} l_{0} ^{2} }}{5} - \frac{{52{\kern 1pt} l_{1} ^{2} }}{5} + x^{2} } \right) \\ & + \frac{{ - 2{\kern 1pt} hx^{2} N\cos \left( \alpha \right)}}{3}\left( {\mu _{1} - \mu _{2} + \frac{{3k_{1} }}{4} + \frac{{ - 3{\kern 1pt} k_{2} }}{4}} \right) + \frac{{ - 11hN\cos \left( \alpha \right)\left( { - \mu _{2} + \mu _{1} } \right)}}{4}\left( {l_{0} ^{2} + \frac{{8{\kern 1pt} l_{1} ^{2} }}{{33}} + \frac{{ - {\kern 1pt} l_{2} ^{2} }}{{11}}} \right) \\ & \left. { - \left( {N + 2} \right)\left( {N\mu _{1} + \mu _{2} } \right)\sin \left( \alpha \right)x\left( {\frac{{ - 3{\kern 1pt} l_{0} ^{2} }}{{10}} + \frac{{ - 16{\kern 1pt} l_{1} ^{2} }}{{15}} + \frac{{{\kern 1pt} l_{2} ^{2} }}{2} + x^{2} } \right)} \right\}, \\ C_{3} = & \frac{h}{{\left( {N + 1} \right)x^{4} \left( {\tan \left( \alpha \right)} \right)^{4} }}\left\{ {\left( {\left( {\left( {\frac{{4x^{2} }}{3} - 2{\kern 1pt} l_{0} ^{2} - 4{\kern 1pt} l_{1} ^{2} } \right)\mu _{1} + x^{2} k_{1} } \right)N + \left( {\frac{{4x^{2} }}{3} - 2{\kern 1pt} l_{0} ^{2} - 4{\kern 1pt} l_{1} ^{2} } \right)\mu _{2} + x^{2} k_{2} } \right)\left( {\tan \left( \alpha \right)} \right)^{2} } \right. \\ & \left. { + \frac{{\left( {18{\kern 1pt} N\mu _{1} + 18{\kern 1pt} \mu _{2} } \right)\left( {l_{0} ^{2} + \frac{{4l_{1} ^{2} }}{3}} \right)}}{5}} \right\},C_{4} = \frac{h}{{\left( {N + 1} \right)x^{4} \left( {\tan \left( \alpha \right)} \right)^{3} }}\left\{ {\left( {\left( {\left( {\frac{{4x^{2} }}{3} - 2{\kern 1pt} l_{0} ^{2} - 4{\kern 1pt} l_{1} ^{2} } \right)\mu _{1} + x^{2} k_{1} } \right)N + \left( {\frac{{4x^{2} }}{3} - 2{\kern 1pt} l_{0} ^{2} - 4{\kern 1pt} l_{1} ^{2} } \right)\mu _{2} + x^{2} k_{2} } \right)} \right. \\ & \left. {\left( {\tan \left( \alpha \right)} \right)^{2} + \frac{{\left( {18{\kern 1pt} N\mu _{1} + 18{\kern 1pt} \mu _{2} } \right)\left( {l_{0} ^{2} + \frac{{4l_{1} ^{2} }}{3}} \right)}}{5}} \right\}, \\ \end{aligned}$$

(94)

$$\begin{aligned} C_{5} = & \frac{{ - 7h\cos \left( \alpha \right)}}{{3x^{4} \left( {\sin \left( \alpha \right)} \right)^{4} \left( {N + 1} \right)}}\left\{ {\left( {\mu _{1} + \frac{{3{\kern 1pt} k_{1} }}{7}} \right)x^{2} N\left( {\cos \left( \alpha \right)} \right)^{2} - \frac{{21{\kern 1pt} N\mu _{1} \left( {\cos \left( \alpha \right)} \right)^{2} }}{5}\left( {l_{0} ^{2} + \frac{{256{\kern 1pt} l_{1} ^{2} }}{{147}} + \frac{{5{\kern 1pt} l_{2} ^{2} }}{{49}}} \right)} \right. \\ & + \left( {\mu _{2} + \frac{{3{\kern 1pt} k_{2} }}{7}} \right)x^{2} \left( {\cos \left( \alpha \right)} \right)^{2} - \frac{{21{\kern 1pt} \mu _{2} \left( {\cos \left( \alpha \right)} \right)^{2} }}{5}\left( {l_{0} ^{2} + \frac{{256{\kern 1pt} l_{1} ^{2} }}{{147}} + \frac{{5{\kern 1pt} l_{2} ^{2} }}{{49}}} \right) - \left( {\mu _{1} + \frac{{3{\kern 1pt} k_{1} }}{7}} \right)x^{2} N + \frac{{87{\kern 1pt} N\mu _{1} }}{{70}}\left( {l_{0} ^{2} + \frac{{136{\kern 1pt} l_{1} ^{2} }}{{87}} + \frac{{5{\kern 1pt} l_{2} ^{2} }}{{29}}} \right) \\ & \left. { - \left( {\mu _{2} + \frac{{3{\kern 1pt} k_{2} }}{7}} \right)x^{2} + \frac{{87{\kern 1pt} \mu _{2} }}{{70}}\left( {l_{0} ^{2} + \frac{{136{\kern 1pt} l_{1} ^{2} }}{{87}} + \frac{{5{\kern 1pt} l_{2} ^{2} }}{{29}}} \right)} \right\}, \\ C_{6} = & \frac{{\left( {\left( {\left( {k_{1} + \frac{{ - 2{\kern 1pt} \mu _{1} }}{3}} \right)x^{2} + \frac{{4{\kern 1pt} \mu _{1} }}{5}\left( {l_{0} ^{2} + 3{\kern 1pt} l_{1} ^{2} } \right)} \right)N + \left( {\frac{{ - 2{\kern 1pt} \mu _{2} }}{3} + k_{2} } \right)x^{2} + \frac{{4{\kern 1pt} \mu _{2} }}{5}\left( {l_{0} ^{2} + 3{\kern 1pt} l_{1} ^{2} } \right)} \right)h}}{{\left( {N + 1} \right)x^{3} \tan \left( \alpha \right)}}, \\ C_{7} = & - \frac{h}{{x^{3} \left( {\tan \left( \alpha \right)} \right)^{2} \left( {N + 2} \right)\left( {N + 1} \right)}}\left\{ {\left( {N + 2} \right)\left( {\frac{{3{\kern 1pt} l_{0} ^{2} }}{{10}} + \frac{{16{\kern 1pt} l_{1} ^{2} }}{{15}} + \frac{{ - {\kern 1pt} l_{2} ^{2} }}{2} + x^{2} } \right)\left( {\tan \left( \alpha \right)} \right)^{2} x\left( {N\mu _{1} + \mu _{2} } \right)} \right. \\ & + \frac{{ - {\kern 1pt} h}}{3}\left( {\mu _{1} - \mu _{2} + \frac{{ - 3{\kern 1pt} k_{1} }}{2} + \frac{{3{\kern 1pt} k_{2} }}{2}} \right)x^{2} N\tan \left( \alpha \right) + \frac{{ - 7h}}{5}\left( { - \mu _{2} + \mu _{1} } \right)\left( {l_{0} ^{2} + \frac{{ - 4{\kern 1pt} l_{1} ^{2} }}{7}} \right)N\tan \left( \alpha \right) \\ & \left. { + \frac{{{\kern 1pt} \left( {27{\kern 1pt} N + 54} \right)}}{{10}}\left( {l_{0} ^{2} + \frac{{8{\kern 1pt} l_{1} ^{2} }}{{81}} - \frac{{5{\kern 1pt} l_{2} ^{2} }}{{27}}} \right)x\left( {N\mu _{1} + \mu _{2} } \right)} \right\}, \\ \end{aligned}$$

(95)

$$\begin{aligned} C_{8} = & \frac{{ - h}}{{x^{4} \left( {\tan \left( \alpha \right)} \right)^{2} \left( {N + 2} \right)\left( {N + 1} \right)}}\left\{ {\left( {N + 2} \right)\left( {\frac{{ - 3{\kern 1pt} l_{0} ^{2} }}{{10}} - \frac{{16{\kern 1pt} l_{1} ^{2} }}{{15}} + \frac{{l_{2} ^{2} }}{2} + x^{2} } \right)\left( {\tan \left( \alpha \right)} \right)^{2} x\left( {N\mu _{1} + \mu _{2} } \right)} \right. \\ & + \frac{{2h}}{3}\left( {\mu _{1} - \mu _{2} + \frac{{3k_{1} }}{4} + \frac{{ - 3{\kern 1pt} k_{2} }}{4}} \right)x^{2} N\tan \left( \alpha \right) + \frac{{7{\kern 1pt} h}}{5}\left( { - \mu _{2} + \mu _{1} } \right)\left( {l_{0} ^{2} + \frac{{ - 4l_{1} ^{2} }}{7}} \right)N\tan \left( \alpha \right) \\ & \left. { + \frac{{{\kern 1pt} \left( {33{\kern 1pt} N + 66} \right)}}{{10}}\left( {l_{0} ^{2} + \frac{{112{\kern 1pt} l_{1} ^{2} }}{{99}} + \frac{{5{\kern 1pt} l_{2} ^{2} }}{{33}}} \right)x\left( {N\mu _{1} + \mu _{2} } \right)} \right\},C_{9} = \frac{{h\left( {N\mu _{1} + \mu _{2} } \right)\left( {207{\kern 1pt} l_{0} ^{2} + 136{\kern 1pt} l_{1} ^{2} + 15{\kern 1pt} l_{2} ^{2} } \right)\cos \left( \alpha \right)}}{{30x^{4} \left( {\sin \left( \alpha \right)} \right)^{4} \left( {N + 1} \right)}}, \\ C_{{10}} = & \frac{{h\left( {N\mu _{1} + \mu _{2} } \right)\left( {27{\kern 1pt} l_{0} ^{2} + 16{\kern 1pt} l_{1} ^{2} + 15{\kern 1pt} l_{2} ^{2} } \right)}}{{30x^{4} \left( {\sin \left( \alpha \right)} \right)^{4} \left( {N + 1} \right)}},C_{{11}} = \frac{{h\left( {N\mu _{1} + \mu _{2} } \right)\left( {27{\kern 1pt} l_{0} ^{2} + 16{\kern 1pt} l_{1} ^{2} + 15{\kern 1pt} l_{2} ^{2} } \right)}}{{30{\kern 1pt} N + 30}}, \\ C_{{12}} = & \frac{{3h}}{{10\left( {\sin \left( \alpha \right)} \right)^{3} x^{3} \left( {N + 2} \right)\left( {N + 1} \right)}}\left\{ {\left( {N + 2} \right)\left( {N\mu _{1} + \mu _{2} } \right)x\left( {l_{0} ^{2} + \frac{{32{\kern 1pt} l_{1} ^{2} }}{9} + \frac{{ - 5l_{2} ^{2} }}{3}} \right)\sin \left( \alpha \right)} \right. \\ & \left. { + 5{\kern 1pt} \cos \left( \alpha \right)\left( {l_{0} ^{2} + \frac{{ - {\kern 1pt} l_{2} ^{2} }}{3}} \right)N\left( { - \mu _{2} + \mu _{1} } \right)h} \right\},C_{{13}} = \frac{{3h}}{{10\left( {\sin \left( \alpha \right)} \right)^{3} x^{4} \left( {N + 2} \right)\left( {N + 1} \right)}}\left\{ {\left( {N + 2} \right)\left( {N\mu _{1} + \mu _{2} } \right)x} \right. \\ & \left. {\left( {l_{0} ^{2} + \frac{{32{\kern 1pt} l_{1} ^{2} }}{9} + \frac{{ - 5l_{2} ^{2} }}{3}} \right)\sin \left( \alpha \right) + \frac{{25}}{2}{\kern 1pt} \left( { - \mu _{2} + \mu _{1} } \right)\cos \left( \alpha \right)\left( {l_{0} ^{2} + \frac{{32{\kern 1pt} l_{1} ^{2} }}{{45}} + \frac{{{\kern 1pt} l_{2} ^{2} }}{5}} \right)Nh} \right\}, \\ C_{{14}} = & \frac{{h\left( {N\mu _{1} + \mu _{2} } \right)\left( {27{\kern 1pt} l_{0} ^{2} + 16{\kern 1pt} l_{1} ^{2} + 15{\kern 1pt} l_{2} ^{2} } \right)}}{{15\left( {N + 1} \right)x^{2} \left( {\sin \left( \alpha \right)} \right)^{2} }},C_{{15}} = \frac{{ - h\left( {N\mu _{1} + \mu _{2} } \right)\left( {9{\kern 1pt} l_{0} ^{2} + 4{\kern 1pt} l_{1} ^{2} - 3{\kern 1pt} l_{2} ^{2} } \right)\cos \left( \alpha \right)}}{{3\left( {\sin \left( \alpha \right)} \right)^{3} \left( {N + 1} \right)x^{3} }}, \\ C_{{16}} = & \frac{{3h}}{{5x^{2} \left( {N + 2} \right)\left( {N + 1} \right)\tan \left( \alpha \right)}}\left\{ {\left( {N + 2} \right)\left( {N\mu _{1} + \mu _{2} } \right)x\left( {l_{0} ^{2} + \frac{{32{\kern 1pt} l_{1} ^{2} }}{9} + \frac{{ - 5{\kern 1pt} l_{2} ^{2} }}{3}} \right)\tan \left( \alpha \right)} \right. \\ & \left. { + \frac{{10h}}{3}\left( {l_{0} ^{2} + \frac{{{\kern 1pt} l_{1} ^{2} }}{2}} \right)N\left( { - \mu _{2} + \mu _{1} } \right)} \right\},C_{{17}} = {\kern 1pt} \frac{{ - h\left( {N\mu _{1} + \mu _{2} } \right)\left( {43{\kern 1pt} l_{0} ^{2} + 24{\kern 1pt} l_{1} ^{2} + 15{\kern 1pt} l_{2} ^{2} } \right)\cos \left( \alpha \right)}}{{10\left( {N + 1} \right)x^{2} \left( {\sin \left( \alpha \right)} \right)^{2} }}, \\ C_{{18}} = & {\kern 1pt} \frac{{ - h\left( {N\mu _{1} + \mu _{2} } \right)\left( {87{\kern 1pt} l_{0} ^{2} + 56{\kern 1pt} l_{1} ^{2} + 15{\kern 1pt} l_{2} ^{2} } \right)\cos \left( \alpha \right)}}{{10\left( {\sin \left( \alpha \right)} \right)^{3} \left( {N + 1} \right)x^{4} }},C_{{19}} = \frac{{ - 2h\left( {N\mu _{1} + \mu _{2} } \right)\left( {l_{0} ^{2} - 2{\kern 1pt} l_{1} ^{2} } \right)}}{{5\left( {N + 1} \right)x\tan \left( \alpha \right)}}, \\ \end{aligned}$$

(96)

$$\begin{aligned} C_{{20}} = & \frac{{ - 3h}}{{10\left( {\sin \left( \alpha \right)} \right)^{2} x^{3} \left( {N + 2} \right)\left( {N + 1} \right)}}\left\{ {\left( {N + 2} \right)\left( {N\mu _{1} + \mu _{2} } \right)x\left( {l_{0} ^{2} + \frac{{32{\kern 1pt} l_{1} ^{2} }}{9} + \frac{{ - 5l_{2} ^{2} }}{3}} \right)\sin \left( \alpha \right)} \right. \\ & \left. { - \frac{{37{\kern 1pt} h\left( { - \mu _{2} + \mu _{1} } \right)N\cos \left( \alpha \right)}}{6}\left( {l_{0} ^{2} + \frac{{8{\kern 1pt} l_{1} ^{2} }}{{111}} - \frac{{15{\kern 1pt} l_{2} ^{2} }}{{37}}} \right)} \right\},C_{{21}} = {\kern 1pt} \frac{{3h}}{{10\left( {N + 1} \right)x^{2} \left( {\sin \left( \alpha \right)} \right)^{2} \left( {N + 2} \right)}}\left\{ {\left( {N + 2} \right)\left( {N\mu _{1} + \mu _{2} } \right)x} \right. \\ & \left. {\left( {l_{0} ^{2} + \frac{{32{\kern 1pt} l_{1} ^{2} }}{9} + \frac{{ - 5{\kern 1pt} l_{2} ^{2} }}{3}} \right)\sin \left( \alpha \right) + \frac{{11}}{3}{\kern 1pt} \left( { - \mu _{2} + \mu _{1} } \right)h\cos \left( \alpha \right)N\left( {l_{0} ^{2} + \frac{{8{\kern 1pt} l_{1} ^{2} }}{{11}} + \frac{{5{\kern 1pt} l_{2} ^{2} }}{{11}}} \right)} \right\},C_{{22}} = \frac{{3h}}{{10x^{4} \left( {\sin \left( \alpha \right)} \right)^{4} \left( {N + 2} \right)\left( {N + 1} \right)}} \\ & \left\{ {\left( {N + 2} \right)\left( {N\mu _{1} + \mu _{2} } \right)x\left( {l_{0} ^{2} + \frac{{32{\kern 1pt} l_{1} ^{2} }}{9} - 5/3{\kern 1pt} l_{2} ^{2} } \right)\sin \left( \alpha \right) + 8{\kern 1pt} \cos \left( \alpha \right)\left( { - \mu _{2} + \mu _{1} } \right)N\left( {l_{0} ^{2} + \frac{{l_{1} ^{2} }}{2}} \right)h} \right\}, \\ C_{{23}} = & \frac{{3h}}{{10x\left( {N + 2} \right)\left( {N + 1} \right)\tan \left( \alpha \right)}}\left\{ {\left( {N + 2} \right)\left( {N\mu _{1} + \mu _{2} } \right)x\left( {l_{0} ^{2} + \frac{{32{\kern 1pt} l_{1} ^{2} }}{9} + \frac{{ - 5{\kern 1pt} l_{2} ^{2} }}{3}} \right)\tan \left( \alpha \right) + \frac{{2Nh}}{3}\left( {l_{0} ^{2} - 2{\kern 1pt} l_{1} ^{2} } \right)\left( { - \mu _{2} + \mu _{1} } \right)} \right\}, \\ C_{{24}} = & \frac{{h\left( {N\mu _{1} + \mu _{2} } \right)}}{{x^{4} \left( {\sin \left( \alpha \right)} \right)^{4} \left( {N + 1} \right)}}\left( {\left( {x^{2} - \frac{{129{\kern 1pt} l_{0} ^{2} }}{{10}} - \frac{{208{\kern 1pt} l_{1} ^{2} }}{{15}} + \frac{{ - 5{\kern 1pt} l_{2} ^{2} }}{2}} \right)\left( {\cos \left( \alpha \right)} \right)^{2} - x^{2} + \frac{{18{\kern 1pt} l_{0} ^{2} }}{5} + \frac{{32{\kern 1pt} l_{1} ^{2} }}{{15}} + 2{\kern 1pt} l_{2} ^{2} } \right), \\ C_{{25}} = & \frac{{ - h\left( {N\mu _{1} + \mu _{2} } \right)\left( {27{\kern 1pt} l_{0} ^{2} + 16{\kern 1pt} l_{1} ^{2} + 15{\kern 1pt} l_{2} ^{2} } \right)}}{{15\left( {N + 1} \right)x^{3} \left( {\sin \left( \alpha \right)} \right)^{2} }},C_{{26}} = \frac{{ - 26{\kern 1pt} h\left( {N\mu _{1} + \mu _{2} } \right)}}{{\left( {5{\kern 1pt} N + 5} \right)x^{2} \tan \left( \alpha \right)}}\left( {l_{0} ^{2} + \frac{{4{\kern 1pt} l_{1} ^{2} }}{{13}}} \right), \\ C_{{27}} = & \frac{{h\left( {N\mu _{1} + \mu _{2} } \right)\left( {27{\kern 1pt} l_{0} ^{2} + 16{\kern 1pt} l_{1} ^{2} + 15{\kern 1pt} l_{2} ^{2} } \right)}}{{15\left( {N + 1} \right)x}}, \\ C_{{28}} = & {\kern 1pt} \frac{{h\left( {30{\kern 1pt} \left( {\cos \left( \alpha \right)} \right)^{2} x^{2} - 48{\kern 1pt} \left( {\cos \left( \alpha \right)} \right)^{2} l_{0} ^{2} - 24{\kern 1pt} \left( {\cos \left( \alpha \right)} \right)^{2} l_{1} ^{2} - 30{\kern 1pt} x^{2} - 27{\kern 1pt} l_{0} ^{2} - 16{\kern 1pt} l_{1} ^{2} - 15{\kern 1pt} l_{2} ^{2} } \right)\left( {N\mu _{1} + \mu _{2} } \right)}}{{30\left( {N + 1} \right)x^{2} \left( {\sin \left( \alpha \right)} \right)^{2} }}, \\ C_{{29}} = & \frac{{h\left( {N\mu _{1} + \mu _{2} } \right)\left( {39{\kern 1pt} l_{0} ^{2} + 52{\kern 1pt} l_{1} ^{2} + 15{\kern 1pt} l_{2} ^{2} } \right)\cos \left( \alpha \right)}}{{15\left( {N + 1} \right)x^{3} \left( {\sin \left( \alpha \right)} \right)^{2} }}, \\ \end{aligned}$$

(97)

$$\begin{aligned} D_{1} &= \frac{{ - 15\cos \left( \alpha \right)M0}}{{2x^{3} \left( {\sin \left( \alpha \right)} \right)^{2} }}\left( {l_{0} ^{2} + \frac{{16{\kern 1pt} l_{1} ^{2} }}{{15}} + \frac{{{\kern 1pt} l_{2} ^{2} }}{5}} \right) + {\kern 1pt} \frac{{\left( {\left( { - 70{\kern 1pt} x^{2} + 432{\kern 1pt} l_{0} ^{2} + 176{\kern 1pt} l_{1} ^{2} + 30{\kern 1pt} l_{2} ^{2} } \right)\left( {\cos \left( \alpha \right)} \right)^{2} + 70{\kern 1pt} x^{2} - 351{\kern 1pt} l_{0} ^{2} - 88{\kern 1pt} l_{1} ^{2} - 15{\kern 1pt} l_{2} ^{2} } \right)M2}}{{30x^{4} \left( {\sin \left( \alpha \right)} \right)^{3} }} \\ + \frac{{M3}}{{x^{2} \sin \left( \alpha \right)}},\\ D_{2} &= {\kern 1pt} \frac{{h^{2} \left( { - \mu _{2} + \mu _{1} } \right)N\left( {27{\kern 1pt} l_{0} ^{2} + 8{\kern 1pt} l_{1} ^{2} + 3{\kern 1pt} l_{2} ^{2} } \right)}}{{6\left( {N + 2} \right)\left( {N + 1} \right)x^{2} \sin \left( \alpha \right)}},\\ D_{3} &= \frac{{3h}}{{5\left( {\sin \left( \alpha \right)} \right)^{3} \left( {N + 1} \right)x^{4} \left( {N + 2} \right)}} \\ & \left( {x\left( {l_{0} ^{2} + \frac{{32{\kern 1pt} l_{1} ^{2} }}{9} + \frac{{ - 5{\kern 1pt} l_{2} ^{2} }}{3}} \right)\left( {N\mu _{1} + \mu _{2} } \right)\left( {N + 2} \right)\sin \left( \alpha \right) + \frac{{45{\kern 1pt} \cos \left( \alpha \right)N\left( { - \mu _{2} + \mu _{1} } \right)h}}{4}\left( {l_{0} ^{2} + \frac{{32{\kern 1pt} l_{1} ^{2} }}{{81}} + \frac{{ - l_{2} ^{2} }}{{27}}} \right)} \right), \\ D_{4} &= \frac{{ - 39{\kern 1pt} h^{3} \left( {N^{3} \mu _{1} + \left( {3{\kern 1pt} \mu _{1} + 3{\kern 1pt} \mu _{2} } \right)N^{2} + \left( {8{\kern 1pt} \mu _{1} + 3{\kern 1pt} \mu _{2} } \right)N + 6{\kern 1pt} \mu _{2} } \right)}}{{\left( {40{\kern 1pt} N + 120} \right)\left( {N + 2} \right)\left( {N + 1} \right)x^{4} \left( {\sin \left( \alpha \right)} \right)^{3} }}\left( {l_{0} ^{2} + \frac{{88{\kern 1pt} l_{1} ^{2} }}{{351}} + \frac{{5{\kern 1pt} l_{2} ^{2} }}{{117}}} \right), \\ D_{5} &= {\kern 1pt} \frac{{ - 3h}}{{10x\tan \left( \alpha \right)\left( {N + 2} \right)\left( {N + 1} \right)}}\left( {x\left( {l_{0} ^{2} + \frac{{32{\kern 1pt} l_{1} ^{2} }}{9} + \frac{{ - 5{\kern 1pt} l_{2} ^{2} }}{3}} \right)\left( {N\mu _{1} + \mu _{2} } \right)\left( {N + 2} \right)\tan \left( \alpha \right) + 4{\kern 1pt} h\left( { - \mu _{2} + \mu _{1} } \right)\left( {l_{0} ^{2} + \frac{{ - {\kern 1pt} l_{1} ^{2} }}{3}} \right)N} \right), \\ D_{6} &= \frac{{ - 9h^{2} \left( {l_{0} ^{2} + \frac{{2{\kern 1pt} l_{1} ^{2} }}{9}} \right)\left( { - \mu _{2} + \mu _{1} } \right)N}}{{5\left( {N + 2} \right)\left( {N + 1} \right)}},\\D_{7} &= {\kern 1pt} \frac{{3h^{3} \left( {\left( {l_{0} ^{2} + \frac{{2{\kern 1pt} l_{1} ^{2} }}{9}} \right)x + \frac{{l_{1} ^{2} }}{{15}}} \right)\left( {N^{3} \mu _{1} + \left( {3{\kern 1pt} \mu _{1} + 3{\kern 1pt} \mu _{2} } \right)N^{2} + \left( {8{\kern 1pt} \mu _{1} + 3{\kern 1pt} \mu _{2} } \right)N + 6{\kern 1pt} \mu _{2} } \right)}}{{5\left( {N + 3} \right)\left( {N + 2} \right)\left( {N + 1} \right)x^{2} }}, \\ D_{8} & = \frac{{ - 9M1}}{{2x^{4} \left( {\sin \left( \alpha \right)} \right)^{2} }}\left( {\left( {l_{0} ^{2} + \frac{{8{\kern 1pt} l_{1} ^{2} }}{{27}} + \frac{{{\kern 1pt} l_{2} ^{2} }}{9}} \right)x + \frac{{4{\kern 1pt} l_{1} ^{2} }}{{75}}} \right),\\ D_{9}&= \frac{{ - 3h}}{{10x^{2} \tan \left( \alpha \right)\left( {N + 2} \right)\left( {N + 1} \right)}} \\ & \left( {x\left( {l_{0} ^{2} + \frac{{32{\kern 1pt} l_{1} ^{2} }}{9} + \frac{{ - 5l_{2} ^{2} }}{3}} \right)\left( {N\mu _{1} + \mu _{2} } \right)\left( {N + 2} \right)\tan \left( \alpha \right) - 10{\kern 1pt} \left( { - \mu _{2} + \mu _{1} } \right)N\left( {l_{0} ^{2} + \frac{{l_{1} ^{2} }}{3}} \right)h} \right), \\ D_{{10}} &= \frac{{\left( {3{\kern 1pt} N^{3} \mu _{1} + 3{\kern 1pt} \left( {3{\kern 1pt} \mu _{1} + 3{\kern 1pt} \mu _{2} } \right)N^{2} + 3{\kern 1pt} \left( {8{\kern 1pt} \mu _{1} + 3{\kern 1pt} \mu _{2} } \right)N + 18{\kern 1pt} \mu _{2} } \right)h^{3} }}{{\left( {40{\kern 1pt} N + 120} \right)\left( {N + 2} \right)\left( {N + 1} \right)x^{4} \left( {\sin \left( \alpha \right)} \right)^{4} }}\left( {l_{0} ^{2} + \frac{{16{\kern 1pt} l_{1} ^{2} }}{{27}} + \frac{{5{\kern 1pt} l_{2} ^{2} }}{9}} \right),\\ D_{{11}} &= \frac{{ - h^{2} \left( { - \mu _{2} + \mu _{1} } \right)N\left( {81{\kern 1pt} l_{0} ^{2} + 8{\kern 1pt} l_{1} ^{2} - 15{\kern 1pt} l_{2} ^{2} } \right)}}{{60{\kern 1pt} x\sin \left( \alpha \right)\left( {N + 2} \right)\left( {N + 1} \right)}}, \\ \end{aligned}$$

(98)

$$\begin{aligned} D_{{12}} = \frac{{ - 6h}}{{\left( {N + 1} \right)x^{4} \tan \left( \alpha \right)\left( {N + 2} \right)}}\left\{ {\frac{{ - h\tan \left( \alpha \right)N}}{9}\left[ {\left( {\mu _{2} + \frac{{ - 3 k_{1} }}{4} + \frac{{3 k_{2} }}{4} - \mu _{1} } \right)x^{2} - \frac{{\left( {81 \mu _{2} - 81 \mu _{1} } \right)\left( {l_{0} ^{2} + \frac{{2l_{1} ^{2} }}{9}} \right)}}{{10}}} \right]} \right. \hfill \\ & \left. { + x\left( {N\mu _{1} + \mu _{2} } \right)\left( {N + 2} \right)\left( {l_{0} ^{2} + \frac{{2l_{1} ^{2} }}{3}} \right)} \right\},D_{{13}} = \frac{{ - 6h}}{{x^{4} \left( {\tan \left( \alpha \right)} \right)^{2} \left( {N + 2} \right)\left( {N + 1} \right)}}\left\{ {\frac{{ - h\tan \left( \alpha \right)N}}{9}} \right. \hfill \\ \left. {\left[ {\left( {\mu _{2} + \frac{{ - 3k_{1} }}{4} + \frac{{3 k_{2} }}{4} - \mu _{1} } \right)x^{2} - \frac{{\left( {81 \mu _{2} - 81 \mu _{1} } \right)\left( {l_{0} ^{2} + \frac{{2l_{1} ^{2} }}{9}} \right)}}{{10}}} \right] + x\left( {N\mu _{1} + \mu _{2} } \right)\left( {N + 2} \right)\left( {l_{0} ^{2} + \frac{{2l_{1} ^{2} }}{3}} \right)} \right\},D_{{14}} = \hfill \\ & \frac{{M0 \left( {63l_{0} ^{2} + 104l_{1} ^{2} + 75l_{2} ^{2} } \right)}}{{30x^{2} \sin \left( \alpha \right)}} + \frac{{ - \left( {\left( {70x^{2} - 351l_{0} ^{2} - 112 l_{1} ^{2} - 15l_{2} ^{2} } \right)\left( {\cos \left( \alpha \right)} \right)^{2} - 70x^{2} + 351l_{0} ^{2} + 88l_{1} ^{2} + 15 l_{2} ^{2} } \right)M1}}{{30x^{4} \left( {\sin \left( \alpha \right)} \right)^{3} }} \hfill \\ + \frac{{M4}}{{x^{2} \sin \left( \alpha \right)}} + \frac{{ - \left( {27l_{0} ^{2} + 32l_{1} ^{2} + 9l_{2} ^{2} } \right)M2\cos \left( \alpha \right)}}{{6x^{3} \left( {\sin \left( \alpha \right)} \right)^{2} }}, \hfill \\ D_{{15}} &= \frac{{ - M0 \left( {30 \left( {\cos \left( \alpha \right)} \right)^{2} x^{2} + 36 \left( {\cos \left( \alpha \right)} \right)^{2} l_{0} ^{2} + 48 \left( {\cos \left( \alpha \right)} \right)^{2} l_{1} ^{2} - 30x^{2} - 63l_{0} ^{2} - 64l_{1} ^{2} - 15l_{2} ^{2} } \right)}}{{30x^{2} \left( {\sin \left( \alpha \right)} \right)^{2} }} \hfill \\ & + \frac{{\left( {100x^{2} - 810l_{0} ^{2} - 198 l_{1} ^{2} } \right)M1}}{{75 x^{4} }} + \frac{{ - 6\left( {l_{0} ^{2} + 4/3 l_{1} ^{2} } \right)M2}}{{5x^{3} \tan \left( \alpha \right)}} + \frac{{M4}}{{x^{2} }},D_{{16}} = \frac{{ - h^{2} \left( { - \mu _{2} + \mu _{1} } \right)N\left( {27 l_{0} ^{2} + 8l_{1} ^{2} + 3 l_{2} ^{2} } \right)}}{{12x^{2} \left( {\sin \left( \alpha \right)} \right)^{2} \left( {N + 2} \right)\left( {N + 1} \right)}}, \hfill \\ D_{{17}} & = \frac{{M0}}{{30x^{3} \left( {\tan \left( \alpha \right)} \right)^{2} }}\left( {30 x\left( {x^{2} + \frac{{3l_{0} ^{2} }}{{10}} + \frac{{16 l_{1} ^{2} }}{{15}} + \frac{{ - l_{2} ^{2} }}{2}} \right)\left( {\tan \left( \alpha \right)} \right)^{2} + 81 x\left( {l_{0} ^{2} + \frac{{8 l_{1} ^{2} }}{{81}} - \frac{{5 l_{2} ^{2} }}{{27}}} \right)} \right) \hfill \\ & + \frac{{\left( {20x^{2} + 324l_{0} ^{2} + 72 l_{1} ^{2} } \right)M2}}{{30x^{3} \tan \left( \alpha \right)}} - \frac{{M3}}{{x\tan \left( \alpha \right)}},D_{{18}} = \frac{{\left( {18l_{0} ^{2} + 4l_{1} ^{2} } \right)M0}}{{5 x^{2} \tan \left( \alpha \right)}} + \frac{{\left( { - 20x^{2} + 162l_{0} ^{2} + 36 l_{1} ^{2} } \right)M2}}{{15x^{3} }} - \frac{{M3}}{x}, \hfill \\ D_{{19}} & = \frac{{ - h^{2} \left( { - \mu _{2} + \mu _{1} } \right)N\left( {81l_{0} ^{2} + 8l_{1} ^{2} - 15 l_{2} ^{2} } \right)}}{{60 x^{3} \left( {\sin \left( \alpha \right)} \right)^{3} \left( {N + 2} \right)\left( {N + 1} \right)}},D_{{20}} = \frac{{\left( {9N^{3} \mu _{1} + 9\left( {3 \mu _{1} + 3 \mu _{2} } \right)N^{2} + 9 \left( {8 \mu _{1} + 3 \mu _{2} } \right)N + 54 \mu _{2} } \right)h^{3} }}{{\left( {40 N + 120} \right)\left( {N + 2} \right)\left( {N + 1} \right)x^{3} \left( {\sin \left( \alpha \right)} \right)^{3} }} \hfill \\ & \left( {l_{0} ^{2} + \frac{{8 l_{1} ^{2} }}{{81}} - \frac{{5 l_{2} ^{2} }}{{27}}} \right),D_{{21}} = \frac{{ - 3h^{3} \left( {N^{3} \mu _{1} + \left( {3 \mu _{1} + 3 \mu _{2} } \right)N^{2} + \left( {8 \mu _{1} + 3 \mu _{2} } \right)N + 6 \mu _{2} } \right)}}{{4\left( {N + 3} \right)\left( {N + 2} \right)\left( {N + 1} \right)x^{2} \sin \left( \alpha \right)}}\left( {l_{0} ^{2} + \frac{{8 l_{1} ^{2} }}{{27}} + \frac{{ l_{2} ^{2} }}{9}} \right), \hfill \\ D_{{22}}& = \frac{{ - h^{2} \left( { - \mu _{2} + \mu _{1} } \right)N\left( {27l_{0} ^{2} + 16l_{1} ^{2} + 15 l_{2} ^{2} } \right)}}{{60 x^{4} \left( {\sin \left( \alpha \right)} \right)^{4} \left( {N + 2} \right)\left( {N + 1} \right)}}, \hfill \\ \end{aligned}$$

(99)

$$\begin{aligned} D_{{23}} &= \frac{{6h}}{{5x^{2} \tan \left( \alpha \right)\left( {N + 2} \right)\left( {N + 1} \right)}}\{ \frac{{ - 5hN\tan \left( \alpha \right)}}{9}[\left( {\mu _{2} + \frac{{ - 3{\kern 1pt} k_{1} }}{4} + \frac{{3{\kern 1pt} k_{2} }}{4} - \mu _{1} } \right)x^{2} + \frac{{\left( {81{\kern 1pt} \mu _{2} - 81{\kern 1pt} \mu _{1} } \right)\left( {l_{0} ^{2} + \frac{{2l_{1} ^{2} }}{9}} \right)}}{{10}}] \\ &\quad + \left( {l_{0} ^{2} + \frac{{ - l_{1} ^{2} }}{3}} \right)\left( {N\mu _{1} + \mu _{2} } \right)x\left( {N + 2} \right)\} , \\ D_{{24}} &= \frac{{h^{2} \left( { - \mu _{2} + \mu _{1} } \right)N\left( {27{\kern 1pt} l_{0} ^{2} + 8{\kern 1pt} l_{1} ^{2} + 3{\kern 1pt} l_{2} ^{2} } \right)}}{{12x^{3} \left( {\sin \left( \alpha \right)} \right)^{2} \left( {N + 2} \right)\left( {N + 1} \right)}},D_{{25}} = \frac{{ - 3h}}{{10x^{3} \left( {\sin \left( \alpha \right)} \right)^{3} \left( {N + 2} \right)\left( {N + 1} \right)}} \\ & \left( {x\left( {l_{0} ^{2} + \frac{{32{\kern 1pt} l_{1} ^{2} }}{9} + \frac{{ - 5{\kern 1pt} l_{2} ^{2} }}{3}} \right)\left( {N\mu _{1} + \mu _{2} } \right)\left( {N + 2} \right)\sin \left( \alpha \right) + 5{\kern 1pt} h\left( {l_{0} ^{2} + \frac{{ - {\kern 1pt} l_{2} ^{2} }}{3}} \right)\left( { - \mu _{2} + \mu _{1} } \right)\cos \left( \alpha \right)N} \right), \\ D_{{26}} &= \frac{{Nh^{2} \left( { - \mu _{2} + \mu _{1} } \right)\left( {351{\kern 1pt} l_{0} ^{2} + 88{\kern 1pt} l_{1} ^{2} + 15{\kern 1pt} l_{2} ^{2} } \right)}}{{60{\kern 1pt} \left( {\sin \left( \alpha \right)} \right)^{3} \left( {N + 1} \right)x^{4} \left( {N + 2} \right)}}, \\ D_{{27}} = & \frac{{\left( { - 315{\kern 1pt} l_{0} ^{2} - 320{\kern 1pt} l_{1} ^{2} - 75{\kern 1pt} l_{2} ^{2} } \right)M0}}{{150{\kern 1pt} x}} + \frac{{\left( { - 200{\kern 1pt} x^{3} + \left( {1620{\kern 1pt} l_{0} ^{2} + 396{\kern 1pt} l_{1} ^{2} } \right)x + 36{\kern 1pt} l_{1} ^{2} } \right)M1}}{{150{\kern 1pt} x^{4} }} - \frac{{M4}}{x}, \\ D_{{28}} = & {\kern 1pt} \frac{{ - 2M0{\kern 1pt} \left( {2{\kern 1pt} l_{1} ^{2} + 3{\kern 1pt} l_{2} ^{2} } \right)}}{{3x^{2} \sin ^{2} \left( \alpha \right)}} + \frac{{M1}}{{x^{4} \left( {\sin \left( \alpha \right)} \right)^{4} }}\left( {\left( {x^{2} + \frac{{99{\kern 1pt} l_{0} ^{2} }}{{10}} + \frac{{122{\kern 1pt} l_{1} ^{2} }}{{75}} + \frac{{ - 3{\kern 1pt} l_{2} ^{2} }}{2}} \right)\left( {\cos \left( \alpha \right)} \right)^{2} - x^{2} - \frac{{99{\kern 1pt} l_{0} ^{2} }}{{10}} - \frac{{122{\kern 1pt} l_{1} ^{2} }}{{75}} + \frac{{l_{2} ^{2} }}{2}} \right) \\ & + {\kern 1pt} \frac{{M2{\kern 1pt} \left( {27{\kern 1pt} l_{0} ^{2} + 16{\kern 1pt} l_{1} ^{2} + 45{\kern 1pt} l_{2} ^{2} } \right)\cos \left( \alpha \right)}}{{15x^{3} \left( {\sin \left( \alpha \right)} \right)^{3} }},D_{{29}} = \frac{{3\left( {N^{3} \mu _{1} + \left( {3{\kern 1pt} \mu _{1} + 3{\kern 1pt} \mu _{2} } \right)N^{2} + \left( {8{\kern 1pt} \mu _{1} + 3{\kern 1pt} \mu _{2} } \right)N + 6{\kern 1pt} \mu _{2} } \right)h^{3} }}{{8\left( {N + 1} \right)\left( {N + 2} \right)\left( {N + 3} \right)x^{2} \left( {\sin \left( \alpha \right)} \right)^{2} }}\left( {l_{0} ^{2} + \frac{{8{\kern 1pt} l_{1} ^{2} }}{{27}} + \frac{{l_{2} ^{2} }}{9}} \right), \\ \end{aligned}$$

(100)

$$\begin{aligned} D_{{30}} = & \frac{{ - M0{\kern 1pt} \left( {21{\kern 1pt} l_{0} ^{2} + 8{\kern 1pt} l_{1} ^{2} - 15{\kern 1pt} l_{2} ^{2} } \right)}}{{10x\sin \left( \alpha \right)}} + {\kern 1pt} \frac{{ - \left( {\left( { - 10{\kern 1pt} x^{2} + 351{\kern 1pt} l_{0} ^{2} + 64{\kern 1pt} l_{1} ^{2} - 15{\kern 1pt} l_{2} ^{2} } \right)\left( {\cos \left( \alpha \right)} \right)^{2} + 10{\kern 1pt} x^{2} - 351{\kern 1pt} l_{0} ^{2} - 88{\kern 1pt} l_{1} ^{2} - 15{\kern 1pt} l_{2} ^{2} } \right)M1}}{{30x^{3} \left( {\sin \left( \alpha \right)} \right)^{3} }} \\ & + \frac{{\left( {3{\kern 1pt} l_{0} ^{2} + 4{\kern 1pt} l_{1} ^{2} - 5{\kern 1pt} l_{2} ^{2} } \right)M2{\kern 1pt} \cos \left( \alpha \right)}}{{5x^{2} \left( {\sin \left( \alpha \right)} \right)^{2} }} - \frac{{M4}}{{x\sin \left( \alpha \right)}}, \\ D_{{31}} = & \frac{{9{\kern 1pt} \left( {N^{3} \mu _{1} + \left( {3{\kern 1pt} \mu _{1} + 3{\kern 1pt} \mu _{2} } \right)N^{2} + \left( {8{\kern 1pt} \mu _{1} + 3{\kern 1pt} \mu _{2} } \right)N + 6{\kern 1pt} \mu _{2} } \right)h^{3} }}{{\left( {40{\kern 1pt} N + 120} \right)\left( {N + 2} \right)\left( {N + 1} \right)x\sin \left( \alpha \right)}}\left( {l_{0} ^{2} + \frac{{8{\kern 1pt} l_{1} ^{2} }}{{81}} - \frac{{5{\kern 1pt} l_{2} ^{2} }}{{27}}} \right),D_{{32}} = \frac{{ - 18{\kern 1pt} h^{2} \left( {l_{0} ^{2} + \frac{{2{\kern 1pt} l_{1} ^{2} }}{9}} \right)\left( { - \mu _{2} + \mu _{1} } \right)N}}{{5{\kern 1pt} x\left( {N + 2} \right)\left( {N + 1} \right)}}, \\ D_{{33}} = & \left( { - \frac{{21{\kern 1pt} l_{0} ^{2} }}{{10}} - \frac{{32{\kern 1pt} l_{1} ^{2} }}{{15}} + \frac{{ - {\kern 1pt} l_{2} ^{2} }}{2}} \right)M0 + \frac{{\left( { - 200{\kern 1pt} x^{3} + \left( { - 1620{\kern 1pt} l_{0} ^{2} - 432{\kern 1pt} l_{1} ^{2} } \right)x - 36{\kern 1pt} l_{1} ^{2} } \right)M1}}{{150{\kern 1pt} x^{3} }} + {\kern 1pt} \frac{{6\left( {l_{0} ^{2} + \frac{{ - {\kern 1pt} l_{1} ^{2} }}{3}} \right)M2}}{{x\tan \left( \alpha \right)}} - M4, \\ D_{{34}} = & \frac{{3\left( {N^{3} \mu _{1} + \left( {3{\kern 1pt} \mu _{1} + 3{\kern 1pt} \mu _{2} } \right)N^{2} + \left( {8{\kern 1pt} \mu _{1} + 3{\kern 1pt} \mu _{2} } \right)N + 6{\kern 1pt} \mu _{2} } \right)\left( {l_{0} ^{2} + 2/9{\kern 1pt} l_{1} ^{2} } \right)h^{3} }}{{10\left( {N + 1} \right)\left( {N + 2} \right)\left( {N + 3} \right)}},D_{{35}} = \frac{{3\left( {l_{0} ^{2} + \frac{{4{\kern 1pt} l_{1} ^{2} }}{9} + \frac{{ - {\kern 1pt} l_{2} ^{2} }}{3}} \right)\cos \left( \alpha \right)M0}}{{x^{2} \left( {\sin \left( \alpha \right)} \right)^{2} }} \\ & + {\kern 1pt} \frac{{\left( {\left( {10{\kern 1pt} x^{2} - 360{\kern 1pt} l_{0} ^{2} - 80{\kern 1pt} l_{1} ^{2} } \right)\left( {\cos \left( \alpha \right)} \right)^{2} - 10{\kern 1pt} x^{2} + 351{\kern 1pt} l_{0} ^{2} + 88{\kern 1pt} l_{1} ^{2} + 15{\kern 1pt} l_{2} ^{2} } \right)M2}}{{30x^{3} \left( {\sin \left( \alpha \right)} \right)^{3} }} - \frac{{M3}}{{x\sin \left( \alpha \right)}},D_{{36}} = \frac{{9{\kern 1pt} \cos \left( \alpha \right)M0}}{{10{\kern 1pt} x^{3} \left( {\sin \left( \alpha \right)} \right)^{3} }} \\ & \left( {l_{0} ^{2} + \frac{{56{\kern 1pt} l_{1} ^{2} }}{{27}} + \frac{{25{\kern 1pt} l_{2} ^{2} }}{9}} \right) + \frac{{M2}}{{30x^{4} \left( {\sin \left( \alpha \right)} \right)^{4} }}\left( {30{\kern 1pt} \left( {x^{2} + \frac{{99{\kern 1pt} l_{0} ^{2} }}{{10}} + \frac{{28{\kern 1pt} l_{1} ^{2} }}{{15}} + \frac{{ - 3l_{2} ^{2} }}{2}} \right)\left( {\cos \left( \alpha \right)} \right)^{2} - 30{\kern 1pt} x^{2} - 297{\kern 1pt} l_{0} ^{2} - 56{\kern 1pt} l_{1} ^{2} + 15{\kern 1pt} l_{2} ^{2} } \right), \\ I_{2} = & \frac{1}{{12}}{\kern 1pt} \rho _{1} h^{3} + \frac{{h^{3} \left( {N^{2} + N + 2} \right)\left( {\rho _{2} - \rho _{1} } \right)}}{{4{\kern 1pt} N^{3} + 24{\kern 1pt} N^{2} + 44{\kern 1pt} N + 24}}, \\ \end{aligned}$$

(101)

$$\begin{gathered} M0 = {\mu_1}h + \frac{{h\left( {{\mu_2} - {\mu_1}} \right)}}{N + 1},M1 = \frac{1}{12}{\kern 1pt} {\mu_1}{h^3} + {\kern 1pt} \frac{{{h^3}\left( {{N^2} + N + 2} \right)\left( {{\mu_2} - {\mu_1}} \right)}}{{4\left( {N + 3} \right)\left( {N + 2} \right)\left( {N + 1} \right)}},M2 = \frac{{{h^2}N\left( {{\mu_2} - {\mu_1}} \right)}}{{2\left( {N + 2} \right)\left( {N + 1} \right)}}, \hfill \\ M3 = {\kern 1pt} \frac{{{h^2}\left( {{k_2} - {k_1}} \right)N}}{{2\left( {N + 2} \right)\left( {N + 1} \right)}},M4 = \frac{1}{12}{\kern 1pt} {k_1}{h^3} + \frac{{{h^3}\left( {{N^2} + N + 2} \right)\left( {{k_2} - {k_1}} \right)}}{{4\left( {N + 3} \right)\left( {N + 2} \right)\left( {N + 1} \right)}},K0 = {k_1}h + \frac{{h\left( {{k_2} - {k_1}} \right)}}{N + 1}. \hfill \\ \end{gathered}$$

(102)

$$\begin{aligned} E_{1} = & \frac{{M1{\kern 1pt} \left( {27{\kern 1pt} l_{0} ^{2} + 16{\kern 1pt} l_{1} ^{2} + 15{\kern 1pt} l_{2} ^{2} } \right)}}{{15x}},E_{2} = \frac{{M1{\kern 1pt} \left( {27{\kern 1pt} l_{0} ^{2} + 16{\kern 1pt} l_{1} ^{2} + 15{\kern 1pt} l_{2} ^{2} } \right)}}{{30}},E_{3} = {\kern 1pt} \frac{{M1{\kern 1pt} \left( {27{\kern 1pt} l_{0} ^{2} + 8{\kern 1pt} l_{1} ^{2} + 3{\kern 1pt} l_{2} ^{2} } \right)}}{{6x^{2} \left( {\sin \left( \alpha \right)} \right)^{2} }}, \\ E_{4} = & \frac{{2M1{\kern 1pt} \left( {9{\kern 1pt} l_{0} ^{2} + 2{\kern 1pt} l_{1} ^{2} } \right)}}{{5x^{4} \left( {\sin \left( \alpha \right)} \right)^{4} }},E_{5} = \frac{{{\kern 1pt} M2{\kern 1pt} \left( {27{\kern 1pt} l_{0} ^{2} + 16{\kern 1pt} l_{1} ^{2} + 15{\kern 1pt} l_{2} ^{2} } \right)}}{{30}},E_{6} = \frac{{M2{\kern 1pt} \left( {27{\kern 1pt} l_{0} ^{2} + 8{\kern 1pt} l_{1} ^{2} + 3{\kern 1pt} l_{2} ^{2} } \right)}}{{6x^{2} \left( {\sin \left( \alpha \right)} \right)^{2} }}, \\ E_{7} = & \frac{{2M2{\kern 1pt} \left( {9{\kern 1pt} l_{0} ^{2} + 2{\kern 1pt} l_{1} ^{2} } \right)}}{{5x^{4} \left( {\sin \left( \alpha \right)} \right)^{4} }},E_{8} = {\kern 1pt} \frac{1}{{30x^{4} \left( {\sin \left( \alpha \right)} \right)^{4} }}\left( { - 9{\kern 1pt} M0{\kern 1pt} x\left( {l_{0} ^{2} + \frac{{32{\kern 1pt} l_{1} ^{2} }}{9} + \frac{{ - 5{\kern 1pt} l_{2} ^{2} }}{3}} \right)\sin \left( \alpha \right) + 144{\kern 1pt} \left( {l_{0} ^{2} + \frac{{{\kern 1pt} l_{1} ^{2} }}{2}} \right)M2{\kern 1pt} \cos \left( \alpha \right)} \right), \\ E_{9} = & \frac{{M2{\kern 1pt} \left( {27{\kern 1pt} l_{0} ^{2} + 16{\kern 1pt} l_{1} ^{2} + 15{\kern 1pt} l_{2} ^{2} } \right)}}{{15x}}, \\ E_{{10}} = & \frac{{M0}}{{x^{4} \left( {\sin \left( \alpha \right)} \right)^{4} }}\left( {\sin \left( \alpha \right)\left( {x^{2} + \frac{{ - 8l_{1} ^{2} }}{3} + 2{\kern 1pt} l_{2} ^{2} } \right)x\left( {\cos \left( \alpha \right)} \right)^{3} - \sin \left( \alpha \right)\left( {x^{2} + \frac{{9{\kern 1pt} l_{0} ^{2} }}{{10}} + \frac{{28{\kern 1pt} l_{1} ^{2} }}{{15}} + \frac{{5{\kern 1pt} l_{2} ^{2} }}{2}} \right)x\cos \left( \alpha \right)} \right), \\ & + \frac{{M2}}{{x^{4} \left( {\sin \left( \alpha \right)} \right)^{4} }}\left( {\left( {x^{2} - 4{\kern 1pt} l_{2} ^{2} } \right)\left( {\cos \left( \alpha \right)} \right)^{4} - 2{\kern 1pt} \left( {x^{2} - \frac{{27{\kern 1pt} l_{0} ^{2} }}{{20}} + \frac{{ - 8{\kern 1pt} l_{1} ^{2} }}{5} + \frac{{ - 11{\kern 1pt} l_{2} ^{2} }}{4}} \right)\left( {\cos \left( \alpha \right)} \right)^{2} + x^{2} - \frac{{27{\kern 1pt} l_{0} ^{2} }}{{10}} + \frac{{ - 8{\kern 1pt} l_{1} ^{2} }}{5} + \frac{{ - 3{\kern 1pt} l_{2} ^{2} }}{2}} \right), \\ E_{{11}} &= \frac{{ - \left( {\left( { - 63{\kern 1pt} l_{0} ^{2} - 104{\kern 1pt} l_{1} ^{2} - 75{\kern 1pt} l_{2} ^{2} } \right)x^{2} \left( {\cos \left( \alpha \right)} \right)^{2} + \left( {63{\kern 1pt} l_{0} ^{2} + 104{\kern 1pt} l_{1} ^{2} + 75{\kern 1pt} l_{2} ^{2} } \right)x^{2} } \right)M0}}{{30x^{4} \sin ^{3} \left( \alpha \right)}} \\ & + \frac{{39{\kern 1pt} \cos \left( \alpha \right)M2}}{{10{\kern 1pt} x^{3} \sin ^{2} \left( \alpha \right)}}\left( {l_{0} ^{2} + \frac{{136{\kern 1pt} l_{1} ^{2} }}{{117}} + \frac{{25{\kern 1pt} l_{2} ^{2} }}{{39}}} \right) + {\kern 1pt} \frac{{ - 1}}{{30x^{4} \sin ^{3} \left( \alpha \right)}}\left[\left( {\left( { - 70{\kern 1pt} M1 - 30{\kern 1pt} M4} \right)x^{2} + 189{\kern 1pt} \left( {l_{0} ^{2} + \frac{{16{\kern 1pt} l_{1} ^{2} }}{{21}} + \frac{{5{\kern 1pt} l_{2} ^{2} }}{9}} \right)M1} \right)\right. \\ & \left. \left( {\cos \left( \alpha \right)} \right)^{2} + \left( {70{\kern 1pt} M1 + 30{\kern 1pt} M4} \right)x^{2} - 189{\kern 1pt} \left( {l_{0} ^{2} + \frac{{8{\kern 1pt} l_{1} ^{2} }}{{21}} + \frac{{5{\kern 1pt} l_{2} ^{2} }}{{21}}} \right)M1\right],E_{{12}} = \frac{{ - M1{\kern 1pt} \left( {27{\kern 1pt} l_{0} ^{2} + 8{\kern 1pt} l_{1} ^{2} + 3{\kern 1pt} l_{2} ^{2} } \right)}}{{6x^{3} \left( {\sin \left( \alpha \right)} \right)^{2} }}, \\ E_{{13}} = & \frac{{M1{\kern 1pt} \left( {81{\kern 1pt} l_{0} ^{2} + 8{\kern 1pt} l_{1} ^{2} - 15{\kern 1pt} l_{2} ^{2} } \right)}}{{30x^{3} \left( {\sin \left( \alpha \right)} \right)^{3} }}, \\ \end{aligned}$$

(103)

$$\begin{aligned} E_{{14}} = & \frac{{ - \left( {63{\kern 1pt} l_{0} ^{2} + 64{\kern 1pt} l_{1} ^{2} + 15{\kern 1pt} l_{2} ^{2} } \right)M0}}{{30x^{2} \left( {\sin \left( \alpha \right)} \right)^{2} }} + \frac{{\left( {\left( {40{\kern 1pt} x^{2} - 27{\kern 1pt} l_{0} ^{2} - 24{\kern 1pt} l_{1} ^{2} + 45{\kern 1pt} l_{2} ^{2} } \right)\left( {\cos \left( \alpha \right)} \right)^{2} - 40{\kern 1pt} x^{2} + 27{\kern 1pt} l_{0} ^{2} - 24{\kern 1pt} l_{1} ^{2} - 45{\kern 1pt} l_{2} ^{2} } \right)M1}}{{30x^{4} \left( {\sin \left( \alpha \right)} \right)^{4} }} \\ & + \frac{{\left( {12{\kern 1pt} l_{0} ^{2} + 16{\kern 1pt} l_{1} ^{2} } \right)\cos \left( \alpha \right)M2}}{{5{\kern 1pt} x^{3} \left( {\sin \left( \alpha \right)} \right)^{3} }} - \frac{{M4}}{{x^{2} \left( {\sin \left( \alpha \right)} \right)^{2} }},E_{{15}} = {\kern 1pt} \frac{{ - \left( {4{\kern 1pt} l_{1} ^{2} + 6{\kern 1pt} l_{2} ^{2} } \right)}}{3}M0 + \frac{{9\cos \left( \alpha \right)M2}}{{5x\sin \left( \alpha \right)}}\left( {l_{0} ^{2} + \frac{{ - 4{\kern 1pt} l_{1} ^{2} }}{{27}} + \frac{{ - 5{\kern 1pt} l_{2} ^{2} }}{9}} \right) \\ & + \frac{{ - \left( {\left( { - 30{\kern 1pt} x^{2} - 81{\kern 1pt} l_{0} ^{2} - 72{\kern 1pt} l_{1} ^{2} - 15{\kern 1pt} l_{2} ^{2} } \right)\left( {\cos \left( \alpha \right)} \right)^{2} + 30{\kern 1pt} x^{2} + 81{\kern 1pt} l_{0} ^{2} + 48{\kern 1pt} l_{1} ^{2} + 45{\kern 1pt} l_{2} ^{2} } \right)M1}}{{30x^{2} \left( {\sin \left( \alpha \right)} \right)^{2} }},E_{{16}} = {\kern 1pt} \frac{{3M2{\kern 1pt} \left( {21{\kern 1pt} l_{0} ^{2} + 8{\kern 1pt} l_{1} ^{2} + 5{\kern 1pt} l_{2} ^{2} } \right)}}{{10x^{4} \left( {\sin \left( \alpha \right)} \right)^{3} }}, \\ E_{{17}} = & \frac{{\left( { - 21{\kern 1pt} l_{0} ^{2} - 8{\kern 1pt} l_{1} ^{2} + 15{\kern 1pt} l_{2} ^{2} } \right)M0}}{{10x\sin \left( \alpha \right)}} + \frac{{\left( {\left( { - 50{\kern 1pt} x^{2} - 945{\kern 1pt} l_{0} ^{2} - 408{\kern 1pt} l_{1} ^{2} - 375{\kern 1pt} l_{2} ^{2} } \right)\left( {\cos \left( \alpha \right)} \right)^{2} + 50{\kern 1pt} x^{2} + 945{\kern 1pt} l_{0} ^{2} + 288{\kern 1pt} l_{1} ^{2} + 225{\kern 1pt} l_{2} ^{2} } \right)M1}}{{150{\kern 1pt} x^{3} \left( {\left( {\cos \left( \alpha \right)} \right)^{2} - 1} \right)\sin \left( \alpha \right)}} \\ & + \frac{{\left( {3{\kern 1pt} l_{0} ^{2} + 4{\kern 1pt} l_{1} ^{2} - 5{\kern 1pt} l_{2} ^{2} } \right)M2{\kern 1pt} \cos \left( \alpha \right)}}{{5x^{2} \left( {\sin \left( \alpha \right)} \right)^{2} }} - \frac{{M4}}{{x\sin \left( \alpha \right)}},E_{{18}} = \frac{{\left( {117{\kern 1pt} l_{0} ^{2} + 176{\kern 1pt} l_{1} ^{2} - 15{\kern 1pt} l_{2} ^{2} } \right)\cos \left( \alpha \right)M0}}{{30x^{3} \left( {\sin \left( \alpha \right)} \right)^{3} }} + \frac{{M3}}{{x^{2} \left( {\left( {\cos \left( \alpha \right)} \right)^{2} - 1} \right)}} \\ & + \frac{{\left( {\left( {40{\kern 1pt} x^{2} - 63{\kern 1pt} l_{0} ^{2} - 48{\kern 1pt} l_{1} ^{2} + 45{\kern 1pt} l_{2} ^{2} } \right)\left( {\cos \left( \alpha \right)} \right)^{2} - 40{\kern 1pt} x^{2} + 27{\kern 1pt} l_{0} ^{2} - 24{\kern 1pt} l_{1} ^{2} - 45{\kern 1pt} l_{2} ^{2} } \right)M2}}{{30x^{4} \left( {\sin \left( \alpha \right)} \right)^{4} }}, \\ E_{{19}} = & \frac{{3M1{\kern 1pt} \left( {21{\kern 1pt} l_{0} ^{2} + 8{\kern 1pt} l_{1} ^{2} + 5{\kern 1pt} l_{2} ^{2} } \right)}}{{10x^{4} \left( {\sin \left( \alpha \right)} \right)^{3} }},E_{{20}} = \frac{{M1{\kern 1pt} \left( {675{\kern 1pt} xl_{0} ^{2} + 200{\kern 1pt} xl_{1} ^{2} + 75{\kern 1pt} xl_{2} ^{2} - 36{\kern 1pt} l_{1} ^{2} } \right)}}{{75{\kern 1pt} x^{3} \sin \left( \alpha \right)}}, \\ E_{{21}} = & {\kern 1pt} \frac{{ - 1}}{{30\left( {\sin \left( \alpha \right)} \right)^{2} x^{2} }}\left( { - 126{\kern 1pt} \left( {l_{0} ^{2} + \frac{{8{\kern 1pt} l_{1} ^{2} }}{{21}} + \frac{{5{\kern 1pt} l_{2} ^{2} }}{{21}}} \right)M2{\kern 1pt} \cos \left( \alpha \right) + 9{\kern 1pt} \left( {l_{0} ^{2} + \frac{{32{\kern 1pt} l_{1} ^{2} }}{9} - 5/3{\kern 1pt} l_{2} ^{2} } \right)x\sin \left( \alpha \right)M0} \right), \\ E_{{22}} = & \frac{1}{{30\left( {\sin \left( \alpha \right)} \right)^{2} x^{3} }}\left( { - 9{\kern 1pt} \left( {l_{0} ^{2} + \frac{{32{\kern 1pt} l_{1} ^{2} }}{9} - 5/3{\kern 1pt} l_{2} ^{2} } \right)x\sin \left( \alpha \right)M0 - 243{\kern 1pt} \cos \left( \alpha \right)M2{\kern 1pt} \left( {l_{0} ^{2} + \frac{{104{\kern 1pt} l_{1} ^{2} }}{{243}} + \frac{{5{\kern 1pt} l_{2} ^{2} }}{{81}}} \right)} \right), \\ \end{aligned}$$

(104)

$$\begin{aligned} E_{{23}} = & \frac{{\left( {9{\kern 1pt} l_{0} ^{2} + 12{\kern 1pt} l_{1} ^{2} - 15{\kern 1pt} l_{2} ^{2} } \right)\cos \left( \alpha \right)M0}}{{10{\kern 1pt} \sin \left( \alpha \right)x}} + \frac{{M2}}{{30\left( {\sin \left( \alpha \right)} \right)^{2} x^{2} }} \\ & \left( {30{\kern 1pt} \left( {x^{2} + 9/5{\kern 1pt} l_{0} ^{2} + \frac{{32{\kern 1pt} l_{1} ^{2} }}{{15}} + l_{2} ^{2} } \right)\left( {\cos \left( \alpha \right)} \right)^{2} - 30{\kern 1pt} x^{2} - 81{\kern 1pt} l_{0} ^{2} - 48{\kern 1pt} l_{1} ^{2} - 45{\kern 1pt} l_{2} ^{2} } \right),E_{{24}} = \frac{{M2{\kern 1pt} \left( {27{\kern 1pt} l_{0} ^{2} + 8{\kern 1pt} l_{1} ^{2} + 3{\kern 1pt} l_{2} ^{2} } \right)}}{{3x^{2} \sin \left( \alpha \right)}}, \\ E_{{25{\kern 1pt} }} = & \frac{{ - M2{\kern 1pt} \left( {27{\kern 1pt} l_{0} ^{2} + 8{\kern 1pt} l_{1} ^{2} + 3{\kern 1pt} l_{2} ^{2} } \right)}}{{6\left( {\sin \left( \alpha \right)} \right)^{2} x^{3} }},E_{{26}} = \frac{{M1{\kern 1pt} \left( {81{\kern 1pt} l_{0} ^{2} + 8{\kern 1pt} l_{1} ^{2} - 15{\kern 1pt} l_{2} ^{2} } \right)}}{{30\sin \left( \alpha \right)x}},E_{{27}} = \frac{{3\cos \left( \alpha \right)M0}}{{10\left( {\sin \left( \alpha \right)} \right)^{2} x^{2} }}\left( {l_{0} ^{2} + \frac{{32{\kern 1pt} l_{1} ^{2} }}{9} - 5/3{\kern 1pt} l_{2} ^{2} } \right) \\ & + \frac{{ - \left( {\left( { - 10{\kern 1pt} x^{2} - 189{\kern 1pt} l_{0} ^{2} - 96{\kern 1pt} l_{1} ^{2} - 75{\kern 1pt} l_{2} ^{2} } \right)\left( {\cos \left( \alpha \right)} \right)^{2} + 10{\kern 1pt} x^{2} + 189{\kern 1pt} l_{0} ^{2} + 72{\kern 1pt} l_{1} ^{2} + 45{\kern 1pt} l_{2} ^{2} } \right)M2}}{{30x^{3} \left( {\sin \left( \alpha \right)} \right)^{3} }} - \frac{{M3}}{{\sin \left( \alpha \right)x}}, \\ E_{{28{\kern 1pt} }} = & \frac{{\left( { - 4{\kern 1pt} l_{1} ^{2} - 6{\kern 1pt} l_{2} ^{2} } \right)M0}}{{3x}} + \frac{{ - \left( {\left( { - 30{\kern 1pt} x^{2} + 81{\kern 1pt} l_{0} ^{2} + 72{\kern 1pt} l_{1} ^{2} + 15{\kern 1pt} l_{2} ^{2} } \right)\left( {\cos \left( \alpha \right)} \right)^{2} + 30{\kern 1pt} x^{2} - 81{\kern 1pt} l_{0} ^{2} - 48{\kern 1pt} l_{1} ^{2} - 45{\kern 1pt} l_{2} ^{2} } \right)M1}}{{30\left( {\sin \left( \alpha \right)} \right)^{2} x^{3} }}, \\ E_{{29}} = & \frac{{9{\kern 1pt} \cos \left( \alpha \right)M0}}{{10{\kern 1pt} x^{2} \sin \left( \alpha \right)}}\left( {l_{0} ^{2} + \frac{{16{\kern 1pt} l_{1} ^{2} }}{{27}} + 5/9{\kern 1pt} l_{2} ^{2} } \right) + {\kern 1pt} \frac{{\left( {30{\kern 1pt} \left( {x^{2} - 8/5{\kern 1pt} l_{1} ^{2} - 3{\kern 1pt} l_{2} ^{2} } \right)\left( {\cos \left( \alpha \right)} \right)^{2} - 30{\kern 1pt} x^{2} + 81{\kern 1pt} l_{0} ^{2} + 48{\kern 1pt} l_{1} ^{2} + 45{\kern 1pt} l_{2} ^{2} } \right)M2}}{{30\left( {\sin \left( \alpha \right)} \right)^{2} x^{3} }}, \\ E_{{30}} = & \frac{{ - M0}}{{x^{3} \left( {\sin \left( \alpha \right)} \right)^{3} }}\left( {\left( {x^{2} - 9/2{\kern 1pt} l_{0} ^{2} - \frac{{28{\kern 1pt} l_{1} ^{2} }}{3} - 1/2{\kern 1pt} l_{2} ^{2} } \right)\left( {\cos \left( \alpha \right)} \right)^{2} - x^{2} } \right) - \frac{{M3{\kern 1pt} \cos \left( \alpha \right)}}{{\left( {\sin \left( \alpha \right)} \right)^{2} x^{2} }} \\ & + {\kern 1pt} \frac{{\left( {\left( {40{\kern 1pt} x^{2} - 189{\kern 1pt} l_{0} ^{2} - 144{\kern 1pt} l_{1} ^{2} + 15{\kern 1pt} l_{2} ^{2} } \right)\left( {\cos \left( \alpha \right)} \right)^{3} + \left( { - 40{\kern 1pt} x^{2} + 189{\kern 1pt} l_{0} ^{2} + 72{\kern 1pt} l_{1} ^{2} - 15{\kern 1pt} l_{2} ^{2} } \right)\cos \left( \alpha \right)} \right)M2}}{{30x^{4} \left( {\sin \left( \alpha \right)} \right)^{4} }}, \\ E_{{31}} = & \frac{{9\cos \left( \alpha \right)M0}}{{2\left( {\sin \left( \alpha \right)} \right)^{2} x^{3} }}\left( {l_{0} ^{2} + \frac{{40{\kern 1pt} l_{1} ^{2} }}{{27}} + 5/9{\kern 1pt} l_{2} ^{2} } \right) + \frac{{ - M3}}{{x^{2} \sin \left( \alpha \right)}} \\ & + \frac{{ - \left( {\left( { - 70{\kern 1pt} x^{2} + 189{\kern 1pt} l_{0} ^{2} + 144{\kern 1pt} l_{1} ^{2} + 105{\kern 1pt} l_{2} ^{2} } \right)\left( {\cos \left( \alpha \right)} \right)^{2} + 70{\kern 1pt} x^{2} - 189{\kern 1pt} l_{0} ^{2} - 72{\kern 1pt} l_{1} ^{2} - 45{\kern 1pt} l_{2} ^{2} } \right)M2}}{{30x^{4} \left( {\sin \left( \alpha \right)} \right)^{3} }}, \\ E_{{32}} = & \frac{{ - M0}}{{\left( {\sin \left( \alpha \right)} \right)^{2} x^{2} }}\left( {\left( {x^{2} - \frac{{9{\kern 1pt} l_{0} ^{2} }}{{10}} - \frac{{16{\kern 1pt} l_{1} ^{2} }}{5} + 3/2{\kern 1pt} l_{2} ^{2} } \right)\left( {\cos \left( \alpha \right)} \right)^{2} - x^{2} - 4/3{\kern 1pt} l_{1} ^{2} - 2{\kern 1pt} l_{2} ^{2} } \right) + \frac{{M1}}{{x^{4} \left( {\sin \left( \alpha \right)} \right)^{4} }} \\ & \left[ {\left( {x^{2} - \frac{{27{\kern 1pt} l_{0} ^{2} }}{{10}} - \frac{{16{\kern 1pt} l_{1} ^{2} }}{{15}} - 5/2{\kern 1pt} l_{2} ^{2} } \right)\left( {\cos \left( \alpha \right)} \right)^{4} + \left( { - 2{\kern 1pt} x^{2} + \frac{{27{\kern 1pt} l_{0} ^{2} }}{5} + 4{\kern 1pt} l_{1} ^{2} + 4{\kern 1pt} l_{2} ^{2} } \right)\left( {\cos \left( \alpha \right)} \right)^{2} + x^{2} - \frac{{27{\kern 1pt} l_{0} ^{2} }}{{10}} - 8/5{\kern 1pt} l_{1} ^{2} - 3/2{\kern 1pt} l_{2} ^{2} } \right] \\ & + \frac{{M2}}{{30x^{3} \left( {\sin \left( \alpha \right)} \right)^{3} }}[27{\kern 1pt} \left( {l_{0} ^{2} - \frac{{40{\kern 1pt} l_{1} ^{2} }}{{27}} + 5/3{\kern 1pt} l_{2} ^{2} } \right)\left( {\cos \left( \alpha \right)} \right)^{3} - 27{\kern 1pt} \left( {l_{0} ^{2} + \frac{{56{\kern 1pt} l_{1} ^{2} }}{{27}} + 5/3{\kern 1pt} l_{2} ^{2} } \right)\cos \left( \alpha \right)], \\ E_{{33}} = & \frac{{M2{\kern 1pt} \left( {81{\kern 1pt} l_{0} ^{2} + 8{\kern 1pt} l_{1} ^{2} - 15{\kern 1pt} l_{2} ^{2} } \right)}}{{30\sin \left( \alpha \right)x}},E_{{34}} = \frac{{M2{\kern 1pt} \left( {81{\kern 1pt} l_{0} ^{2} + 8{\kern 1pt} l_{1} ^{2} - 15{\kern 1pt} l_{2} ^{2} } \right)}}{{30x^{3} \left( {\sin \left( \alpha \right)} \right)^{3} }}. \\ \end{aligned}$$

(105)