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Journal of Mathematical Sciences

, Volume 227, Issue 4, pp 419–441 | Cite as

Integrable Motions of a Pendulum in a Two-Dimensional Plane

  • M. V. Shamolin
Article
  • 23 Downloads

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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Authors and Affiliations

  1. 1.Institute of Mechanics of the M. V. Lomonosov Moscow State UniversityMoscowRussia

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