الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
In this thesis, we study a mechanical integrable system consisting of a particle carrying an electric charge and moving under a uniform and central field in addition to a magnetic field. The equation of motion which describes the motion of the particle involve five parameters. The main results of the thesis can be summarized in obtaining the equilibrium positions of the particle in two cases, the first case when the magnetic field vanishes and the other case when the problem has in symmetry (due to the existence of cyclic coordinate) under the action of the previous field. Also we study the stability of these positions. We focus our study in the next two parts of the thesis on the second case. We find the solutions of the equations of motion in the plane of polar coordinates and study the trajectory of the motion of the particle. Also we study the phase space flow of the particle and the foliation of the phase space by invariant surfaces. According to Liouville Arnold theorem, these surfaces are tori or cylinders or a union of these surfaces