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Vestnik SamGU. Estestvenno-Nauchnaya Ser., 2015, Issue 10(132), Pages 91–113
(Mi vsgu486)
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This article is cited in 5 scientific papers (total in 5 papers)
Mechanics
Cases of integrability corresponding to the pendulum motion on the plane
M. V. Shamolin Institute of Mechanics, Lomonosov Moscow State University, 1, Leninskie Gory, Moscow, 119192, Russian Federation
(published under the terms of the Creative Commons Attribution 4.0 International License)
Abstract:
In this article, we systemize the results on the study of plane-parallel motion equations of fixed rigid body-pendulum which is placed in certain nonconservative force field. In parallel, we consider the problem of a plane-parallel motion of a free rigid body which is also placed in a similar force field. Thus, the non-conservative tracking force operates onto this body. That force forces the value of certain point of a body to be constant for all the time of a motion, which means the existence of nonintegrable servoconstraint in the system. The obtained results are systematized and served in the invariant form. We also show the nontrivial topological and mechanical analogies.
Keywords:
rigid body, resisting medium, dynamical system, phase pattern, case of integrability.
Received: 18.09.2015
Citation:
M. V. Shamolin, “Cases of integrability corresponding to the pendulum motion on the plane”, Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2015, no. 10(132), 91–113
Linking options:
https://www.mathnet.ru/eng/vsgu486 https://www.mathnet.ru/eng/vsgu/y2015/i10/p91
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Abstract page: | 175 | Full-text PDF : | 50 | References: | 75 |
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