Zuza A. Polynomial solutions for differential equations of solid body dynamics

Dissertation is devoted to constructing new specific solution for polynomial type of Goryachev-Steklov-Kovalevskij classes (class I), Dokshevich (class II) and Chaplygin differential equations of the problem for gyrostat movement in the field of potential and gyroscopic forcos (problem I) and solutions for the classes I, II of gyrostat movement equations in the magnetic field taking into account Barnette-London effect (problem II). By means of the method of invariant correlations the four novel given solutions for the class I and one novel specific solutions for the class II is constructed. In case of reducing central Newton force field to gravity force field the differential equations to the problem I and problem II is produced. The analogues for P.V.Kharlamov equations are developed. Estimate of maximum powers for polynoms solutions of Chaplygin class under one restriction to diagonal elements of the matrix characterising Newtoon gravity in the problem I provided is given, and impossibility of considered variants is proved. Jho novel solutions in each classes I, II for movement equations are constructed in the problem II.