On a Class of Solutions for the Dynamic Equations of a Rigid Body Acted upon by Potential and Gyroscopic Forces

Abstract

The reduction of the Grioli equations to the Yehia equations is obtained by means of nonsingular transformation. A class of solutions for equations of the motion of a rigid body acted upon by potential and gyroscopic forces is given as dependent on the random vector function of components from the unit vector of the symmetry axis of force fields. Asymptotic Lyapunov solutions are considered for the cases where the limit solution is described by a linear vector function.