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CASES OF INTEGRABILITY CORRESPONDING TO THE PENDULUM MOTION IN FOUR-DIMENSIONAL SPACE
- Authors: Shamolin M.V.1
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Affiliations:
- Institute of Mechanics, Lomonosov Moscow State University
- Issue: Vol 23, No 1 (2017)
- Pages: 41-58
- Section: Articles
- URL: https://journals.ssau.ru/est/article/view/5145
- DOI: https://doi.org/10.18287/2541-7525-2017-23-1-41-58
- ID: 5145
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Abstract
In this article, we systemize some results on the study of the equations of motion of dynamically symmetric fixed four-dimensional rigid bodies–pendulums located in a nonconservative force fields. The form of these equations is taken from the dynamics of real fixed rigid bodies placed in a homogeneous flow of a medium. In parallel, we study the problem of the motion of a free four-dimensional rigid body also located in a similar force fields. Herewith, this free rigid body is influenced by a nonconservative tracing force; under action of this force, either the magnitude of the velocity of some characteristic point of the body remains constant, which means that the system possesses a nonintegrable servo constraint. We also show the nontrivial topological and mechanical analogies.
About the authors
M. V. Shamolin
Institute of Mechanics, Lomonosov Moscow State University
Author for correspondence.
Email: morenov@ssau.ru
Russian Federation
References
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