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Contemporary Mathematics and Its Applications, 2016, Volume 100, Pages 36–57 (Mi cma406)  

Integrable motions of a pendulum in a two-dimensional plane

M. V. Shamolin

Lomonosov Moscow State University, Institute of Mechanics

Abstract: In this paper, we examine new cases of integrability of dynamical systems on the tangent bundle to a low-dimensional sphere, including flat dynamical systems that describe a rigid body in a nonconservative force field. The problems studied are described by dynamical systems with variable dissipation with zero mean. We detect cases of integrability of equations of motion in transcendental functions (in terms of classification of singularity) that are expressed through finite combinations of elementary functions.

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English version:
Journal of Mathematical Sciences, 2017, 227:4, 419–441

Document Type: Article
UDC: 517.9+531.01

Citation: M. V. Shamolin, “Integrable motions of a pendulum in a two-dimensional plane”, Contemporary Mathematics and Its Applications, 100 (2016), 36–57; Journal of Mathematical Sciences, 227:4 (2017), 419–441

Citation in format AMSBIB
\Bibitem{Sha16}
\by M.~V.~Shamolin
\paper Integrable motions of a pendulum in a two-dimensional plane
\jour Contemporary Mathematics and Its Applications
\yr 2016
\vol 100
\pages 36--57
\mathnet{http://mi.mathnet.ru/cma406}
\transl
\jour Journal of Mathematical Sciences
\yr 2017
\vol 227
\issue 4
\pages 419--441
\crossref{https://doi.org/10.1007/s10958-017-3595-x}


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