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Journal of Mathematical Sciences

, Volume 236, Issue 6, pp 687–701 | Cite as

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

  • M. V. Shamolin
Article
  • 9 Downloads

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.

Keywords and phrases

dynamical system dissipation transcendental first integral integrability 

AMS Subject Classification

34Cxx 37E10 37N05 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.M. V. Lomonosov Moscow State UniversityMoscowRussia

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