Geometric mechanics on nonholonomic submanifolds

Olga Krupková

Communications in Mathematics (2010)

  • Volume: 18, Issue: 1, page 51-77
  • ISSN: 1804-1388

Abstract

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In this survey article, nonholonomic mechanics is presented as a part of geometric mechanics. We follow a geometric setting where the constraint manifold is a submanifold in a jet bundle, and a nonholonomic system is modelled as an exterior differential system on the constraint manifold. The approach admits to apply coordinate independent methods, and is not limited to Lagrangian systems under linear constraints. The new methods apply to general (possibly nonconservative) mechanical systems subject to general (possibly nonlinear) nonholonomic constraints, and admit a straightforward generalization to higher order mechanics and field theory. In particular, we are concerned with the following topics: the geometry of nonholonomic constraints, equations of motion of nonholonomic systems on constraint manifolds and their geometric meaning, a nonholonomic variational principle, symmetries, a nonholonomic Noether theorem, regularity, and nonholonomic Hamilton equations.

How to cite

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Krupková, Olga. "Geometric mechanics on nonholonomic submanifolds." Communications in Mathematics 18.1 (2010): 51-77. <http://eudml.org/doc/196870>.

@article{Krupková2010,
abstract = {In this survey article, nonholonomic mechanics is presented as a part of geometric mechanics. We follow a geometric setting where the constraint manifold is a submanifold in a jet bundle, and a nonholonomic system is modelled as an exterior differential system on the constraint manifold. The approach admits to apply coordinate independent methods, and is not limited to Lagrangian systems under linear constraints. The new methods apply to general (possibly nonconservative) mechanical systems subject to general (possibly nonlinear) nonholonomic constraints, and admit a straightforward generalization to higher order mechanics and field theory. In particular, we are concerned with the following topics: the geometry of nonholonomic constraints, equations of motion of nonholonomic systems on constraint manifolds and their geometric meaning, a nonholonomic variational principle, symmetries, a nonholonomic Noether theorem, regularity, and nonholonomic Hamilton equations.},
author = {Krupková, Olga},
journal = {Communications in Mathematics},
keywords = {jet bundle; canonical distribution; non-holonomic variational principle; Hamilton equation},
language = {eng},
number = {1},
pages = {51-77},
publisher = {University of Ostrava},
title = {Geometric mechanics on nonholonomic submanifolds},
url = {http://eudml.org/doc/196870},
volume = {18},
year = {2010},
}

TY - JOUR
AU - Krupková, Olga
TI - Geometric mechanics on nonholonomic submanifolds
JO - Communications in Mathematics
PY - 2010
PB - University of Ostrava
VL - 18
IS - 1
SP - 51
EP - 77
AB - In this survey article, nonholonomic mechanics is presented as a part of geometric mechanics. We follow a geometric setting where the constraint manifold is a submanifold in a jet bundle, and a nonholonomic system is modelled as an exterior differential system on the constraint manifold. The approach admits to apply coordinate independent methods, and is not limited to Lagrangian systems under linear constraints. The new methods apply to general (possibly nonconservative) mechanical systems subject to general (possibly nonlinear) nonholonomic constraints, and admit a straightforward generalization to higher order mechanics and field theory. In particular, we are concerned with the following topics: the geometry of nonholonomic constraints, equations of motion of nonholonomic systems on constraint manifolds and their geometric meaning, a nonholonomic variational principle, symmetries, a nonholonomic Noether theorem, regularity, and nonholonomic Hamilton equations.
LA - eng
KW - jet bundle; canonical distribution; non-holonomic variational principle; Hamilton equation
UR - http://eudml.org/doc/196870
ER -

References

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