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Optimization of the motion in a resistant medium of a body with a movable internal mass

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Abstract

The motion, in a resistant medium, of a system consisting of a rigid body and movable internal mass is considered. The external medium acts on the body by a force that piecewise linearly depends on its speed. The class of periodic motions of the internal mass for which the speed of this mass relative to the body is piecewise constant is studied. It is shown that, under certain conditions, the forward movement of the whole system in the medium is possible. The average speed of this movement over a period is determined. Optimal parameters of the motion of the internal mass for which the average speed of the system movement is maximal are found.

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References

  1. F. L. Chernousko, Dokl. Akad. Nauk 405(1), 56 (2005).

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  2. F. L. Chernousko, in Proceedings of Intern. Seminar on Control Theory and Theory of Generalized Solutions of Hamilton-Jacobi Equations, Ekaterinburg, June 22–26, 2005 (Ekaterinburg, Izd. UrO RNA, 2006), Vol. 1, pp. 55–66.

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  3. H. Li, K. Furuta, and F. L. Chernousko, in: Proceedings of Intern. Conf. on Physics and Control, St. Petersburg, Russia, 2003, pp. 15–17.

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Authors and Affiliations

  1. Institute for Problems in Mechanics, the Russian Academy of Sciences, pr. Vernadskogo 101-1, Moscow, 119526, Russia

    F. L. Chernousko

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  1. F. L. Chernousko
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Original Russian Text © F.L. Chernousko, 2006, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2006, Vol. 12, No. 1.

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Chernousko, F.L. Optimization of the motion in a resistant medium of a body with a movable internal mass. Proc. Steklov Inst. Math. 253 (Suppl 1), S76–S82 (2006). https://doi.org/10.1134/S0081543806050063

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  • DOI: https://doi.org/10.1134/S0081543806050063

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