In this review, we discuss new cases of integrable systems on the tangent bundles of finite-dimensional 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
Dynamical system, Integrability, Transcendental first integral
Cite this paper
Maxim V. Shamolin. (2021) Integrability of Differential Equations of Motion of an n-Dimensional Rigid Body in Nonconservative Fields for n = 5 and n = 6. International Journal of Mathematical and Computational Methods, 6, 28-40
Copyright © 2021 Author(s) retain the copyright of this article.
This article is published under the terms of the Creative Commons Attribution License 4.0