Tulczyjew's Triplet for Lie Groups III : Higher Order Dynamics and Reductions for Iterated Bundles

Abstract

Given a Lie group $G$, we elaborate the dynamics on $T^{\ast }{T}^{\ast }G$ and $T^{\ast }TG$, which is given by a Hamiltonian, as well as the dynamics on the Tulczyjew symplectic space $T{T}^{\ast }G$, which may be defined by a Lagrangian or a Hamiltonian function. As the trivializations we adapted respect the group structures of the iterated bundles, we exploit all possible subgroup reductions (Poisson, symplectic or both) of higher order dynamics.

arXiv admin note: substantial text overlap with arXiv:1503.06568

References in corpus (3)

• Tulczyjew's Triplet for Lie Groups II: Dynamics
• On the Geometry of Cotangent Bundles of Lie Groups
• Tulczyjew's Triplet with an Ehresmann connection I: Trivialization and Reduction