Sessions of the Workshop of the Mathematics and Mechanics Department of Lomonosov Moscow State University, “Urgent Problems of Geometry and Mechanics” Named After V. V. Trofimov

摘要

Many problems of multi-dimensional dynamics give rise to mechanical systems whose position space are finite-dimensional spheres. Therefore, tangent bundles of these spheres become the phase spaces of such systems. For example, we can consider a physical pendulum on a cylindrical hinge in a plane-parallel force field on its phase cylinder, and the study of a spatial (three-dimensional) pendulum on a spherical hinge leads to a dynamical system on the tangent bundle of the two-dimensional sphere. The author has previously considered problems related to the dynamics of an n-dimensional rigid body in a nonconservative force field that generated systems on the tangent bundle of the (n — l)-dimensional sphere. The main focus of the work is the inductive transition from systems on the tangent bundles of spheres of low dimensions to systems on the tangent bundle to spheres of any dimension.