Integrable Motions of a Pendulum in a Two-Dimensional Plane
- Authors: Shamolin M.V.1
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Affiliations:
- Institute of Mechanics of the M. V. Lomonosov Moscow State University
- Issue: Vol 227, No 4 (2017)
- Pages: 419-441
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/240156
- DOI: https://doi.org/10.1007/s10958-017-3595-x
- ID: 240156
Cite item
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.
About the authors
M. V. Shamolin
Institute of Mechanics of the M. V. Lomonosov Moscow State University
Author for correspondence.
Email: shamolin@rambler.ru
Russian Federation, Moscow