On a Method for Integrating the Equations of Rigid Body Motion in Three Homogeneous Force Fields

This paper presents a method for integrating the equations of motion of a rigid body having a fixed point in three homogeneous force fields. It is assumed that under certain conditions these equations admit an invariant relation that is characterized by the following property: the velocity of proper rotation of the body is twice as large as the velocity of precession. The integration of the initial system is reduced to the study of three algebraic equations for the main variables of the problem and one differential first-order equation with separating variables.