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@article{1217938,
author = {Čech, Michal and Musilová, Jana},
article_location = {Ostrava, CR},
article_number = {2},
keywords = {nonholonomic mechanical systems; nonholonomic constraint submanifold; canonical},
language = {eng},
issn = {1804-1388},
journal = {Communications in Mathematics},
title = {Symmetries and currents in nonholonomic mechanics},
volume = {22/2014},
year = {2014}
}
TY - JOUR
ID - 1217938
AU - Čech, Michal - Musilová, Jana
PY - 2014
TI - Symmetries and currents in nonholonomic mechanics
JF - Communications in Mathematics
VL - 22/2014
IS - 2
SP - 159-184
EP - 159-184
PB - Ostravska univerzita v Ostrave
SN - 18041388
KW - nonholonomic mechanical systems
KW - nonholonomic constraint submanifold
KW - canonical
N2 - 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. Moreover, the expressions for two other currents are obtained. The corresponding constraint symme- tries are not symmetries of nonholonomic equations of motion. The physical interpretation of results is emphasized.
ER -
ČECH, Michal a Jana MUSILOVÁ. Symmetries and currents in nonholonomic mechanics. \textit{Communications in Mathematics}. Ostrava, CR: Ostravska univerzita v Ostrave, roč.~22/2014, č.~2, s.~159-184. ISSN~1804-1388. 2014.
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