Integrable Systems in the Dynamics on the Tangent Bundle of a Two-Dimensional Sphere / M. V. Shamolin. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2016. № 2. P. 25-30 [Moscow Univ. Mech. Bulletin. Vol. 72, N 2, 2017. P. 27-32].
A mechanical system whose phase space is the tangent bundle of a two-dimensional sphere is studied. The potential nonconservative systems describing a geodesic flow are classified. A multiparameter family of systems possessing a complete set of transcendental first integrals expressed in terms of finite combinations of elementary functions is found. Some examples illustrating the spatial dynamics of a rigid body interacting with a medium are discussed.
Key words: variable dissipation system, dynamic equations, integrability, transcendental first integral.