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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.
  • 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. (en)
Title
  • Geometric mechanics on nonholonomic submanifolds
  • Geometric mechanics on nonholonomic submanifolds (en)
skos:prefLabel
  • Geometric mechanics on nonholonomic submanifolds
  • Geometric mechanics on nonholonomic submanifolds (en)
skos:notation
  • RIV/61988987:17310/10:A12013M3!RIV12-GA0-17310___
http://linked.open...avai/riv/aktivita
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  • P(GA201/09/0981)
http://linked.open...iv/cisloPeriodika
  • 1
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  • 260651
http://linked.open...ai/riv/idVysledku
  • RIV/61988987:17310/10:A12013M3
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  • Jet bundle; holonomic constraint; nonholonomic constraint; the constraint distribution; generalized D?Alembert principle; Chetaev equations; reduced equations; the nonholonomic first variation formula; symmetry; nonholonomic Noether theorem; regularity; nonholonomic Hamilton equations. (en)
http://linked.open.../riv/klicoveSlovo
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  • CZ - Česká republika
http://linked.open...ontrolniKodProRIV
  • [BAD82C5FAC4B]
http://linked.open...i/riv/nazevZdroje
  • Communications in Mathematics
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http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 18
http://linked.open...iv/tvurceVysledku
  • Krupková, Olga
issn
  • 1804-1388
number of pages
http://localhost/t...ganizacniJednotka
  • 17310
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