Matched pairs of discrete dynamical systems
arXiv:1809.00521
Abstract
Matched pairs of Lie groupoids and Lie algebroids are studied. Discrete Euler-Lagrange equations are written for the matched pairs of Lie groupoids. As such, a geometric framework to analyse a discrete system by decomposing it into two mutually interacting subsystems is established. Two examples are provided to illustrate this strategy; the discrete dynamics on the trivial groupoid, and the discrete dynamics on the special linear group.
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References in corpus (8)
- Discrete time Lagrangian mechanics on Lie groups, with an application to the Lagrange top
- Discrete Lagrangian and Hamiltonian Mechanics on Lie groupoids
- Symmetry reduction of discrete Lagrangian mechanics on Lie groups
- Discrete Nonholonomic Lagrangian Systems on Lie Groupoids
- Discrete Routh Reduction
- Discrete Lagrangian field theories on Lie groupoids
- Higher-order discrete variational problems with constraints
- The inverse problem of the calculus of variations for discrete systems