Journal of Symplectic Geometry
Volume 8 (2010)
Discrete Hamilton-Pontryagin mechanics and generating functions on Lie groupoids
Pages: 225 – 238
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.