Discrete Lagrangian and Hamiltonian Mechanics on Lie groupoids

Details Discrete Lagrangian and Hamiltonian Mechanics on Lie groupoids Discrete Lagrangian and Hamiltonian Mechanics on Lie groupoids

2005-06-15

arxiv.org/abs/math/0506299v2

Mathematics

Differential Geometry

38 pages

Scientific paper

10.1088/0951-7715/19/6/006

The purpose of this paper is to describe geometrically discrete Lagrangian and Hamiltonian Mechanics on Lie groupoids. From a variational principle we derive the discrete Euler-Lagrange equations and we introduce a symplectic 2-section, which is preserved by the Lagrange evolution operator. In terms of the discrete Legendre transformations we define the Hamiltonian evolution operator which is a symplectic map with respect to the canonical symplectic 2-section on the prolongation of the dual of the Lie algebroid of the given groupoid. The equations we get include as particular cases the classical discrete Euler-Lagrange equations, the discrete Euler-Poincar\'e and discrete Lagrange-Poincar\'e equations. Our results can be important for the construction of geometric integrators for continuous Lagrangian systems.

Affiliated with

Also associated with

No associations

Rating

Discrete Lagrangian and Hamiltonian Mechanics on Lie groupoids does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Discrete Lagrangian and Hamiltonian Mechanics on Lie groupoids, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Discrete Lagrangian and Hamiltonian Mechanics on Lie groupoids will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-288817