Hamilton’s principle and the rolling motion of a symmetric ball
- Autores: Borisov A.V.1,2, Kilin A.A.2, Mamaev I.S.3,4
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Afiliações:
- Blagonravov Mechanical Engineering Research Institute of RAS
- Udmurt State University
- Institute of Mathematics and Mechanics of the Ural Branch of RAS
- Kalashnikov Izhevsk State Technical University
- Edição: Volume 62, Nº 6 (2017)
- Páginas: 314-317
- Seção: Mechanics
- URL: https://journals.rcsi.science/1028-3358/article/view/191706
- DOI: https://doi.org/10.1134/S1028335817060052
- ID: 191706
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Resumo
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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