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


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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.

Sobre autores

A. Borisov

Blagonravov Mechanical Engineering Research Institute of RAS; Udmurt State University

Autor responsável pela correspondência
Email: borisov@rcd.ru
Rússia, Moscow, 117334; Izhevsk, 426034

A. Kilin

Udmurt State University

Email: borisov@rcd.ru
Rússia, Izhevsk, 426034

I. Mamaev

Institute of Mathematics and Mechanics of the Ural Branch of RAS; Kalashnikov Izhevsk State Technical University

Email: borisov@rcd.ru
Rússia, Ekaterinburg, 620990; Izhevsk, 426069

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