Discrete Hamilton-Pontryagin mechanics and generating functions on Lie groupoids

Abstract

We present a discrete analog of the recently introduced Hamilton-Pontryagin variational principle in Lagrangian mechanics. This unifies two, previously disparate approaches to discrete Lagrangian mechanics: either using the discrete Lagrangian to define a finite version of Hamilton's action principle, or treating it as a symplectic generating function. This is demonstrated for a discrete Lagrangian defined on an arbitrary Lie groupoid; the often encountered special case of the pair groupoid (or Cartesian square) is also given as a worked example.

14 pages; minor revision of section 2.3 to provide more background; major revision of sections 3-4 to allow for several time steps; accepted, Journal of Symplectic Geometry

References in corpus (1)

• Discrete Nonholonomic Lagrangian Systems on Lie Groupoids

Cited by in corpus (6)

• Nonassociative analogs of Lie groupoids
• Relative Geodesics in the Special Euclidean Group
• Discrete dynamics in implicit form
• Discrete mechanics on unitary octonions
• Lagrangian Mechanics and Reduction on Fibered Manifolds
• Discrete Hamiltonian Variational Integrators