Discrete Lagrangian reduction, discrete Euler-Poincare equations, and semidirect products

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dc.creatorBobenko, Alexander I.
dc.creatorSuris, Yuri B.
dc.date1999-06-15
dc.date.accessioned2026-07-07T05:29:32Z
dc.date.available2026-07-07T05:29:32Z
dc.descriptionA discrete version of Lagrangian reduction is developed in the context of discrete time Lagrangian systems on $G\times G$, 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 $G$. In 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.
dc.description16 pp., LaTeX
dc.identifierhttps://arxiv.org/abs/math/9906108
dc.identifierhttp://arxiv.org/abs/math/9906108
dc.identifierLett. Math. Phys., 1999, V. 49, p.79-93.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/78675
dc.subjectSymplectic Geometry
dc.subjectMathematical Physics
dc.subjectDynamical Systems
dc.titleDiscrete Lagrangian reduction, discrete Euler-Poincare equations, and semidirect products
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