Lie algebroids and mechanics

Paulette Libermann

Archivum Mathematicum (1996)

  • Volume: 032, Issue: 3, page 147-162
  • ISSN: 0044-8753

Abstract

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We give a formulation of certain types of mechanical systems using the structure of groupoid of the tangent and cotangent bundles to the configuration manifold M ; the set of units is the zero section identified with the manifold M . We study the Legendre transformation on Lie algebroids.

How to cite

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Libermann, Paulette. "Lie algebroids and mechanics." Archivum Mathematicum 032.3 (1996): 147-162. <http://eudml.org/doc/247853>.

@article{Libermann1996,
abstract = {We give a formulation of certain types of mechanical systems using the structure of groupoid of the tangent and cotangent bundles to the configuration manifold $M$; the set of units is the zero section identified with the manifold $M$. We study the Legendre transformation on Lie algebroids.},
author = {Libermann, Paulette},
journal = {Archivum Mathematicum},
keywords = {Lie groupoid; Lie algebroid; constrained mechanical system; Legendre transformation; time-independent Lagrangian systems; hyperregular Lagrangian; constrained Hamilton equations; constrained Lagrange equations; Legendre transformation; constraint submanifold},
language = {eng},
number = {3},
pages = {147-162},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Lie algebroids and mechanics},
url = {http://eudml.org/doc/247853},
volume = {032},
year = {1996},
}

TY - JOUR
AU - Libermann, Paulette
TI - Lie algebroids and mechanics
JO - Archivum Mathematicum
PY - 1996
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 032
IS - 3
SP - 147
EP - 162
AB - We give a formulation of certain types of mechanical systems using the structure of groupoid of the tangent and cotangent bundles to the configuration manifold $M$; the set of units is the zero section identified with the manifold $M$. We study the Legendre transformation on Lie algebroids.
LA - eng
KW - Lie groupoid; Lie algebroid; constrained mechanical system; Legendre transformation; time-independent Lagrangian systems; hyperregular Lagrangian; constrained Hamilton equations; constrained Lagrange equations; Legendre transformation; constraint submanifold
UR - http://eudml.org/doc/247853
ER -

References

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