The following general procedure can be followed to derive the differential model using Lagrangian mechanics on a coordinate neighborhood of a smooth -dimensional manifold:
(13.137) |
The equations in (13.109) can be alternatively derived using the Euler-Lagrange equation. Let , and let to conform to the notation used to express the Lagrangian.
The kinetic energy is the sum of kinetic energies due to linear and angular velocities, respectively. This yields
(13.138) |
Suppose that generalized forces , , and can be applied to the configuration variables. Applying the Euler-Lagrange equation to yields
Steven M LaValle 2020-08-14