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New Examples of Integrable Systems with Dissipation on the Tangent Bundles of Multidimensional Spheres

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Abstract

In many problems of multidimensional dynamics, systems appear whose state spaces are spheres of finite dimension. Clearly, phase spaces of such systems are tangent bundles of these spheres. In this paper, we examine nonconservative force fields in the dynamics of a multidimensional rigid body in which the system possesses a complete set of first integrals that can be expressed as finite combinations of elementary transcendental functions. We consider the case where the moment of nonconservative forces depends on the tensor of angular velocity.

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Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, Moscow, Russia

    M. V. Shamolin

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  1. M. V. Shamolin
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Correspondence to M. V. Shamolin.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 137, Mathematical Physics, 2017.

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Shamolin, M.V. New Examples of Integrable Systems with Dissipation on the Tangent Bundles of Multidimensional Spheres. J Math Sci 236, 687–701 (2019). https://doi.org/10.1007/s10958-018-4140-2

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  • DOI: https://doi.org/10.1007/s10958-018-4140-2

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