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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 137, Pages 104–117
(Mi into208)
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This article is cited in 1 scientific paper (total in 1 paper)
New cases of integrable systems with dissipation on tangent bundles of multidimensional spheres
M. V. Shamolin Lomonosov Moscow State University, Institute of Mechanics
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 field 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:
dynamical system, dissipation, transcendental first integral, integrability.
Citation:
M. V. Shamolin, “New cases of integrable systems with dissipation on tangent bundles of multidimensional spheres”, Differential equations. Mathematical physics, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 137, VINITI, Moscow, 2017, 104–117; J. Math. Sci. (N. Y.), 236:6 (2019), 687–701
Linking options:
https://www.mathnet.ru/eng/into208 https://www.mathnet.ru/eng/into/v137/p104
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Abstract page: | 201 | Full-text PDF : | 64 | First page: | 6 |
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