Suslov problem with the Clebsch-Tisserand potential. (English) Zbl 1434.70036
Summary: In this paper, we study a nonholonomic mechanical system, namely, the Suslov problem with the Clebsch-Tisserand potential. We analyze the topology of the level sets defined by the integrals in two ways: using an explicit construction and as a consequence of the Poincaré-Hopf theorem. We describe the flow on such manifolds.
MSC:
| 70F25 | Nonholonomic systems related to the dynamics of a system of particles |
| 70G40 | Topological and differential topological methods for problems in mechanics |
| 37J60 | Nonholonomic dynamical systems |
| 37J35 | Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests |
Keywords:
Suslov problem; topology of level sets; nonholonomic systems; rigid body; Chaplygin systemsReferences:
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