Tulczyjew's Triplet for Lie Groups II: Dynamics

Abstract

Taking configuration space as a Lie group, the trivialized Euler-Lagrange and Hamilton's equations are obtained and presented as Lagrangian submanifolds of the trivialized Tulczyjew's symplectic space. Euler-Poincaré and Lie-Poisson equations are presented as Lagrangian submanifolds of the reduced Tulczyjew's symplectic space. Tulczyjew's generalized Legendre transformations for trivialized and reduced dynamics are constructed.

40 pages

References in corpus (1)

• The Geometry and Dynamics of Interacting Rigid Bodies and Point Vortices

Cited by in corpus (1)

• Contact Dynamics versus Legendrian and Lagrangian Submanifolds