. SG ] 1 5 Ju n 19 99 Discrete Lagrangian reduction , discrete Euler – Poincaré equations , and semidirect products
نویسنده
چکیده
A discrete version of Lagrangian reduction is developed in 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. 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. E–mail: bobenko @ math.tu-berlin.de E–mail: suris @ sfb288.math.tu-berlin.de
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