XXVI Workshop on Geometric Methods in Physics 1-7.07.2007

Alexander Burov

Rigid Body Dynamics in a three-dimensional sphere in the central "Newtonian" field

Dynamics of a rigid body embedded into a three-dimensional sphere in the spherical analog of the field of Newtonian attraction is considered. the equations of motion are simplified within the assumption on smallness of the body with respect to the radius of the sphere. The partial separation of motions similar to that one, known in the satellite dynamics is discussed. In particular, the analog of the so-called "Beletsky equation" describing in plane oscillations of a satellite in an elliptic orbit is obtained and studied.