Publication details
Symmetries and currents in nonholonomic mechanics
| Authors | |
|---|---|
| Year of publication | 2014 |
| Type | Article in Periodical |
| Magazine / Source | Communications in Mathematics |
| MU Faculty or unit | |
| Citation | |
| Field | Theoretical physics |
| Keywords | nonholonomic mechanical systems; nonholonomic constraint submanifold; canonical |
| Description | 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. |
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