Symmetries and conservation laws for the Chaplygin sleigh. (English) Zbl 1379.70048
Balan, Vladimir (ed.) et al., Proceedings of the international conference on differential geometry and dynamical systems (DGDS-2014), Mangalia, Romania, September 1–4, 2014. Bucharest: Geometry Balkan Press. BSG Proceedings 22, 7-17 (2015).
Summary: The Chaplygin sleigh is a mechanical system subject to one
linear nonholonomic constraint enforcing the plane motion. We solve equations of motion and study symmetries and conservation laws for this system after deriving general equations of nonholonomic symmetries of the
constraint Lagrangian. Our considerations are based on an efficient geometrical theory on fibred manifolds first presented and developed by Olga
Rossi (Krupková). The obtained results are thoroughly discussed from
the point of view of physics.
For the entire collection see [Zbl 1327.00034].
For the entire collection see [Zbl 1327.00034].
MSC:
| 70G45 | Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics |
| 70H33 | Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics |
| 53B50 | Applications of local differential geometry to the sciences |
