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Integrability of some classes of dynamic systems in terms of elementary functions

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Moscow University Mechanics Bulletin Aims and scope

Abstract

The results of this paper are due to some previous studies of the application problem of motion of a rigid body in a resisting medium. During these studies, a transcendental integral expressed in terms of elementary functions was obtained for a particular case. This fact allowed one to completely analyze all phase trajectories and to indicate those properties that were “rough” and were retained for some more general systems. The integrability of such a system is related to latent symmetries. Therefore, the study of sufficiently wide classes of dynamic systems with similar symmetries is of interest.

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References

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119899, Russia

    M. V. Shamolin

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  1. M. V. Shamolin
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Original Russian Text © M.V. Shamolin, 2008, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2008, Vol. 63, No. 3, pp. 43–49.

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Shamolin, M.V. Integrability of some classes of dynamic systems in terms of elementary functions. Moscow Univ. Mech. Bull. 63, 53–59 (2008). https://doi.org/10.3103/S0027133008030011

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  • DOI: https://doi.org/10.3103/S0027133008030011

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