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.
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
\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}
Linking options:
https://www.mathnet.ru/eng/cma406
https://www.mathnet.ru/eng/cma/v100/p36
This publication is cited in the following 1 articles:
M. V. Shamolin, “Examples of Integrable Systems with Dissipation on the Tangent Bundles of Multidimensional Spheres”, J. Math. Sci. (N. Y.), 250:6 (2020), 932–941
Citation in format AMSBIB
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