Abstract
The dynamic equation of motion of a multi-particle conservative system is obtained using either D’Alembert-Lagrange equation (2.62) or the General Euler-Lagrange (2.76) which in both cases would get the form given in (2.78): \(H({\varvec{q}})\ddot{\varvec{q}}+ C({\varvec{q}},{\dot{{\varvec{q}}}}){\dot{{\varvec{q}}}} + {\varvec{g}}({\varvec{q}}) = {\varvec{\tau }}\).
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Notes
- 1.
In the algebra for this reduction the Lie bracket property of cross matrix expression has been used: \(\left[ {\varvec{a}} \times \right] \left[ {\varvec{b}} \times \right] - \left[ {\varvec{b}} \times \right] \left[ {\varvec{a}} \times \right] = \left[ ({\varvec{a}} \times {\varvec{b}}) \times \right] \).
- 2.
Not to be confused with inertial force, which is a force expressed with inertial frame coordinates w.r.t. the origin of the inertial frame.
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Olguín Díaz, E. (2019). Lagrangian Formulation. In: 3D Motion of Rigid Bodies. Studies in Systems, Decision and Control, vol 191. Springer, Cham. https://doi.org/10.1007/978-3-030-04275-2_7
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DOI: https://doi.org/10.1007/978-3-030-04275-2_7
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