الفهرس 
IntroductionOnly 14 pages are availabe for public view
 |  | from | 107 |  |  |
| | | from | 107 | | |
Abstract
In this thesis we studied the problem of the stability of the periodic motion of a rigid body about a fixed point under its own weight in the case of Bobylev-Steklov, reduced the Euler-Poisson equations to a single second order differential equation in two geometrical variables, earlier introduced by Yehia in 1983. The motion under consideration is a periodic motion. It can be represented by the motion on a closed path on Poisson sphere. By using the method of linear approximation, we obtained the variational equation near the motion under study in several forms, each one has its own advantages, the algebraic form represent Fuch equation, which is used to get particular algebraic solutions by benefiting from known results about Heun’s equation which has fewer regular singular points. Variational equation with periodic coefficients allows the application of Floquet theory. We reduce the study of stability of the periodic motion to the determination of primitive periodic solutions to the variational equation and set of points in the space of parameters which divides space into zones of stability and zones of instability.