Discrete lagrangian reduction, discrete Euler-Poincaré equations, and semidirect products

Alexander I. Bobenko, Yuri B. Suris

Research output: Contribution to journalArticlepeer-review

53 Scopus citations

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 languageEnglish
Pages (from-to)79-93
Number of pages15
JournalLetters in Mathematical Physics
Volume49
Issue number1
DOIs
StatePublished - 1 Jul 1999
Externally publishedYes

Keywords

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

Fingerprint

Dive into the research topics of 'Discrete lagrangian reduction, discrete Euler-Poincaré equations, and semidirect products'. Together they form a unique fingerprint.

Cite this