## Abstract

A discrete version of Lagrangian reduction is developed within the context of discrete time Lagrangian systems on G × G, where G is a Lie group. We consider the case when the Lagrange function is invariant with respect to the action of an isotropy subgroup of a fixed element in the representation space of G. Within this context, the reduction of the discrete Euler-Lagrange equations is shown to lead to the so-called discrete Euler-Poincaré equations. A constrained variational principle is derived. The Legendre transformation of the discrete Euler-Poincaré equations leads to discrete Hamiltonian (Lie-Poisson) systems on a dual space to a semiproduct Lie algebra.

Original language | English |
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Pages (from-to) | 79-93 |

Number of pages | 15 |

Journal | Letters in Mathematical Physics |

Volume | 49 |

Issue number | 1 |

DOIs | |

State | Published - 1 Jul 1999 |

Externally published | Yes |

## Keywords

- Difference equations
- Discretization
- Lagrangian reduction
- Lagrangian system on Lie groups