Vestnik SamU. Estestvenno-Nauchnaya Ser., 2017, Issue 1, Pages 41–58
Cases of integrability corresponding to the pendulum motion in four-dimensional space
M. V. Shamolin
Institute of Mechanics, Lomonosov Moscow State University, 1, Leninskie Gory, Moscow, 119192, Russian Federation
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.
four-dimensional rigid body, non-conservative force field, dynamical system, case of integrability.
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M. V. Shamolin, “Cases of integrability corresponding to the pendulum motion in four-dimensional space”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 2017, no. 1, 41–58
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\paper Cases of integrability corresponding to the pendulum motion in four-dimensional space
\jour Vestnik SamU. Estestvenno-Nauchnaya Ser.
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