Dynamics of finite‐dimensional mechanical systems on Galilean manifolds

Abstract

AbstractAs presented in the related PAMM contribution ‘Kinematics of finite‐dimensional mechanical systems on Galilean manifolds’, the state space of a time‐dependent finite‐dimensional mechanical system is defined as an affine subbundle of the tangent bundle to the Galilean manifold modeling the generalized space‐time of the system. The second‐order vector field on the state space that describes the system's motion can be associated with a differential two‐form called the action form of the mechanical system. In this paper, we postulate the action form for time‐dependent finite‐dimensional mechanical systems. Moreover, we show that Lagrange's equations of the second kind can be derived as a chart representation of the conditions that define the second‐order vector field which describes the motion.