Variational reduction of lagrangian systems with general constraints

In this paper we present an alternative procedure for reducing, in the Lagrangian formalism, the equations of motion of first order constrained mechanical systems with symmetry. The procedure involves two principal connections: one of them is used to define the reduced degrees of freedom and the oth...

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Publicado: 2012
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_19414889_v4_n1_p49_Grillo
http://hdl.handle.net/20.500.12110/paper_19414889_v4_n1_p49_Grillo
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_19414889_v4_n1_p49_Grillo
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spelling paper:paper_19414889_v4_n1_p49_Grillo2023-06-08T16:32:20Z Variational reduction of lagrangian systems with general constraints In this paper we present an alternative procedure for reducing, in the Lagrangian formalism, the equations of motion of first order constrained mechanical systems with symmetry. The procedure involves two principal connections: one of them is used to define the reduced degrees of freedom and the other one to decompose variations into horizontal and vertical components. On the one hand, we show that this new procedure is particularly useful when the configuration space is a trivial principal bundle over the symmetry group, which is the case of many interesting examples. On the other hand, based on that procedure, we extend in a natural way the variational reduction methods to the Lagrangian systems with higher order constraints. Examples are discussed in order to illustrate the involved theorethical constructions. © American Institute of Mathematical Sciences. 2012 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_19414889_v4_n1_p49_Grillo http://hdl.handle.net/20.500.12110/paper_19414889_v4_n1_p49_Grillo
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description In this paper we present an alternative procedure for reducing, in the Lagrangian formalism, the equations of motion of first order constrained mechanical systems with symmetry. The procedure involves two principal connections: one of them is used to define the reduced degrees of freedom and the other one to decompose variations into horizontal and vertical components. On the one hand, we show that this new procedure is particularly useful when the configuration space is a trivial principal bundle over the symmetry group, which is the case of many interesting examples. On the other hand, based on that procedure, we extend in a natural way the variational reduction methods to the Lagrangian systems with higher order constraints. Examples are discussed in order to illustrate the involved theorethical constructions. © American Institute of Mathematical Sciences.
title Variational reduction of lagrangian systems with general constraints
spellingShingle Variational reduction of lagrangian systems with general constraints
title_short Variational reduction of lagrangian systems with general constraints
title_full Variational reduction of lagrangian systems with general constraints
title_fullStr Variational reduction of lagrangian systems with general constraints
title_full_unstemmed Variational reduction of lagrangian systems with general constraints
title_sort variational reduction of lagrangian systems with general constraints
publishDate 2012
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_19414889_v4_n1_p49_Grillo
http://hdl.handle.net/20.500.12110/paper_19414889_v4_n1_p49_Grillo
_version_ 1768542007799578624

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