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.

arXiv comment40 pages

References in corpus (2)

• The Geometry and Dynamics of Interacting Rigid Bodies and Point Vortices
• On the geometry of higher-order variational problems on Lie groups

Cited by in corpus (4)

• A review on coisotropic reduction in Symplectic, Cosymplectic, Contact and Co-contact Hamiltonian systems
• Contact Dynamics versus Legendrian and Lagrangian Submanifolds
• Tulczyjew's Triplet for Lie Groups III : Higher Order Dynamics and Reductions for Iterated Bundles
• The Tulczyjew triple in mechanics on a Lie group