Symmetries and currents in nonholonomic mechanics

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F14%3A00074352" target="_blank" >RIV/00216224:14310/14:00074352 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Symmetries and currents in nonholonomic mechanics

Popis výsledku v původním jazyce

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 basedon 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.

Název v anglickém jazyce

Symmetries and currents in nonholonomic mechanics

Popis výsledku anglicky

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 basedon 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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BE - Teoretická fyzika

OECD FORD obor

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Projekt

<a href="/cs/project/GA14-02476S" target="_blank" >GA14-02476S: Variace, geometrie a fyzika</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2014

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Communications in Mathematics

ISSN

1804-1388

e-ISSN

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Svazek periodika

22/2014

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

26

Strana od-do

159-184

Kód UT WoS článku

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EID výsledku v databázi Scopus

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