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  • In this paper we derive general equations for constraint Noether- -type symmetries of a rst order non-holonomic mechanical system and the corresponding currents, i.e. functions constant along trajectories of the nonholonomic system. The approach is based on a consistent and very ef- fective geometrical theory of nonholonomic constrained systems on bred manifolds and their jet prolongations, rst presented and developed by Olga Rossi. As a representative example of application of the geometrical theory and the equations of symmetries and conservation laws derived within this framework we present the Chaplygin sleigh. It is a mechanical system sub- ject to one linear nonholonomic constraint enforcing the plane motion. We describe the trajectories of the Chaplygin sleigh and show that the usual kinetic energy conservation law holds along them, the time translation gen- erator being the corresponding constraint symmetry and simultaneously the symmetry of nonholonomic equations of motion.
  • In this paper we derive general equations for constraint Noether- -type symmetries of a rst order non-holonomic mechanical system and the corresponding currents, i.e. functions constant along trajectories of the nonholonomic system. The approach is based on a consistent and very ef- fective geometrical theory of nonholonomic constrained systems on bred manifolds and their jet prolongations, rst presented and developed by Olga Rossi. As a representative example of application of the geometrical theory and the equations of symmetries and conservation laws derived within this framework we present the Chaplygin sleigh. It is a mechanical system sub- ject to one linear nonholonomic constraint enforcing the plane motion. We describe the trajectories of the Chaplygin sleigh and show that the usual kinetic energy conservation law holds along them, the time translation gen- erator being the corresponding constraint symmetry and simultaneously the symmetry of nonholonomic equations of motion. (en)
Title
  • Symmetries and currents in nonholonomic mechanics
  • Symmetries and currents in nonholonomic mechanics (en)
skos:prefLabel
  • Symmetries and currents in nonholonomic mechanics
  • Symmetries and currents in nonholonomic mechanics (en)
skos:notation
  • RIV/00216224:14310/14:00074352!RIV15-GA0-14310___
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GA14-02476S)
http://linked.open...iv/cisloPeriodika
  • 2
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 48877
http://linked.open...ai/riv/idVysledku
  • RIV/00216224:14310/14:00074352
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • nonholonomic mechanical systems; nonholonomic constraint submanifold; canonical (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • CZ - Česká republika
http://linked.open...ontrolniKodProRIV
  • [3DCC2F8E2758]
http://linked.open...i/riv/nazevZdroje
  • Communications in Mathematics
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 22/2014
http://linked.open...iv/tvurceVysledku
  • Musilová, Jana
  • Čech, Michal
issn
  • 1804-1388
number of pages
http://localhost/t...ganizacniJednotka
  • 14310
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