1 Erratum to: Celest Mech Dyn Astr (2014) 118:253–271 DOI 10.1007/s10569-014-9531-1

Pg. 258. The equation for \({\hat{S}}\) should be

$$\begin{aligned} {\hat{S}}={\hat{W}}\times {\hat{R}} \end{aligned}$$

Pg. 260. Equation 6 should not have an initial minus sign. The \({\hat{P}}\) term should have a minus sign, and the \({\hat{Q}}\) symbol should be within the parentheses.

$$\begin{aligned} {\mathop {v}\limits ^{\rightharpoonup }}_{{\textit{chf}}_{\textit{PQW}\,2}}=\sqrt{\frac{\mu }{p_{\textit{chf}}}} \left( {-\sin (\nu _2){\hat{P}}+\left( {e_{\textit{chf}} +\cos (\nu _2)}\right) {\hat{Q}}}\right) \end{aligned}$$

Pg. 260. Equation 10 should have a cosine in the middle term denominator:

$$\begin{aligned} \frac{{\mathop {v}\limits ^{\rightharpoonup }}_{{\textit{dep}}_{\textit{SEZ}}}(e)}{\left| {{\mathop {r}\limits ^{\rightharpoonup }}_{{\textit{dep}}_{\textit{RSW}1}}}\right| \cos (\Delta \phi _{\textit{dep}})}r_{\textit{chf}2} -{\mathop {v}\limits ^{\rightharpoonup }}_{{\textit{chf}}_{\textit{RSW}1}}(s) \end{aligned}$$

Pg. 262. Unnumbered equation before equation 15 should not have the arcsine in the first line.

$$\begin{aligned} \Delta \phi _{\textit{dep}} =\left( {\frac{z}{r_{\textit{chf}2} }} \right) \end{aligned}$$

Pg. 262 Unnumbered equation before equation 17.

  • The first line should have a minus sign in the front and should use \(r_{chf2}\) for consistency;

    $$\begin{aligned} -\frac{\dot{z}}{r_{\textit{chf}\,2}}\frac{{\mathop {r}\limits ^{\rightharpoonup }}_{{\textit{dep}}_{\textit{SEZ}}}\left( z\right) }{\hat{{r}}_{{\textit{dep}}_{\textit{SEZ}}}\left( z\right) } \end{aligned}$$

  • In the second line, the \(r_{\textit{chf}2}\) should be moved from within the first parenthesis term, to the last term;

    $$\begin{aligned} \left( {\dot{y}+{\mathop {v}\limits ^{\rightharpoonup }}_{{\textit{chf}}_{\textit{RSW}1}}\left( s\right) } \right) \frac{{\mathop {r}\limits ^{\rightharpoonup }}_{{\textit{dep}}_{\textit{SEZ}} } \left( z\right) }{\hat{{r}}_{{\textit{dep}}_{\textit{SEZ}}}\left( z \right) }\frac{\cos \left( {\Delta \phi _{\textit{dep}}}\right) }{r_{chf\,2}} \end{aligned}$$