Variational reduction of Hamiltonian systems with general constraints

JOURNAL OF GEOMETRY AND PHYSICS

卷:144

Article

Grillo, Sergio D.¹  Salomone, Leandro M.²  Zuccalli, Marcela² 

[1] UN Cuyo CNEA, Inst Balseiro, San Carlos De Bariloche, Rio Negro, Argentina

[2] UNLP, Fac Ciencias Exactas, Ctr Matemat La Plata, La Plata, Buenos Aires, Argentina

关键词: Symmetry;    Reduction;    Constraint;    Hamiltonian;    Systems;   

DOI  :  10.1016/j.geomphys.2019.05.009

来源: Elsevier

【 摘 要 】

In the Hamiltonian formalism, and in the presence of a symmetry Lie group, a variational reduction procedure has already been developed for Hamiltonian systems without constraints. In this paper we present a procedure of the same kind, but for the entire class of the higher order constrained systems (HOCS), described in the Hamiltonian formalism. Last systems include the standard and generalized nonholonomic Hamiltonian systems as particular cases. When restricted to Hamiltonian systems without constraints, our procedure gives rise exactly to the so-called Hamilton-Poincare equations, as expected. In order to illustrate the procedure, we study in detail the case in which both the configuration space of the system and the involved symmetry define a trivial principal bundle. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free