New Cases of Integrability of Systems of Geodesics and Potential and Dissipative Systems on Tangent Bundles of Finite-Dimensional Manifolds

M. V. Shamolin^a^,*

^aLomonosov Moscow State University, Moscow, 119192 Russia

Correspondence to: *e-mail: shamolin@imec.msu.ru

Received 27 April, 2021

Abstract—The integrability of certain classes of homogeneous geodesic, potential, and dissipative dynamical systems on the tangent bundles of finite-dimensional manifolds is shown. In this case, the force fields lead to variable-sign dissipation and generalize previously considered fields.

Keywords: dynamical system, geodesics, potential, integrability, dissipation, transcendental first integral

DOI: 10.1134/S1064562421050148