Shctetinina O. New solution of Kirchhoff, Grioli equations of a problem about gyrostat movement under the influence of potential and gyroscopic forces

The thesis is devoted to solving problems of integration of the Kirchhoff equations and the Grioli equations. The main goal of our investigations is to construct new solutions of the generalized equations of rigid body dynamics with the help of the Jacobi integrating factor theory, invariant relations (IR) method, and on the basis of properties of gyrostat motions. New solutions are obtained in cases of one IR. New solutions of the Kirchhoff equations are constructed in cases of three linear and rational IR. Conditions of the existence of three IR of a special type for the Grioli equations are investigated. New solutions of the Kirchhoff equations for gyrostat precessions around the vertical and around an inclined axis are constructed. New classes of isoconic motions are obtained. Asymptotic motions of a spherical gyrostat are studied.