Doklady Physics

, Volume 62, Issue 6, pp 314–317 | Cite as

Hamilton’s principle and the rolling motion of a symmetric ball

Mechanics
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Abstract

In this paper, we show that the trajectories of a dynamical system with nonholonomic constraints can satisfy Hamilton’s principle. As the simplest illustration, we consider the problem of a homogeneous ball rolling without slipping on a plane. However, Hamilton’s principle is formulated either for a reduced system or for a system defined in an extended phase space. It is shown that the dynamics of a nonholonomic homogeneous ball can be embedded in a higher-dimensional Hamiltonian phase flow. We give two examples of such an embedding: embedding in the phase flow of a free system and embedding in the phase flow of the corresponding vakonomic system.

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Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Blagonravov Mechanical Engineering Research Institute of RASMoscowRussia
  2. 2.Udmurt State UniversityIzhevskRussia
  3. 3.Institute of Mathematics and Mechanics of the Ural Branch of RASEkaterinburgRussia
  4. 4.Kalashnikov Izhevsk State Technical UniversityIzhevskRussia

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