Low-Dimensional and Multi-Dimensional Pendulums in Nonconservative Fields. Part 1
- Authors: Shamolin M.V.1
-
Affiliations:
- Institute of Mechanics of the M. V. Lomonosov Moscow State University
- Issue: Vol 233, No 2 (2018)
- Pages: 173-299
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/241558
- DOI: https://doi.org/10.1007/s10958-018-3933-7
- ID: 241558
Cite item
Abstract
In this review, we discuss new cases of integrable systems on the tangent bundles of finitedimensional spheres. Such systems appear in the dynamics of multidimensional rigid bodies in nonconservative fields. These problems are described by systems with variable dissipation with zero mean. We found several new cases of integrability of equations of motion in terms of transcendental functions (in the sense of the classification of singularities) that can be expressed as 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@imec.msu.ru
Russian Federation, Moscow