Variational reduction of Hamiltonian systems with general constraints
| Autor: | Sergio Daniel Grillo, Leandro Salomone, Marcela Zuccalli |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Nonholonomic system
010102 general mathematics Constraint (computer-aided design) FOS: Physical sciences General Physics and Astronomy Lie group Mathematical Physics (math-ph) 01 natural sciences Principal bundle Symmetry (physics) Hamiltonian system ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION 0103 physical sciences 010307 mathematical physics Geometry and Topology Configuration space 0101 mathematics Mathematics::Symplectic Geometry Mathematical Physics Hamiltonian (control theory) MathematicsofComputing_DISCRETEMATHEMATICS Mathematics Mathematical physics |
| Zdroj: | Journal of Geometry and Physics. 144:209-234 |
| ISSN: | 0393-0440 |
| DOI: | 10.1016/j.geomphys.2019.05.009 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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