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Remarks on the covering of the possible motion area by solutions in rigid body systems. (English) Zbl 1446.70013
In the present paper, the motion of a rigid body with a fixed point is considered. The main purpose is the study of the covering of the possible motion area in the integrable cases of Lagrange and Kovalevskaya. The solutions of the system after Routh reduction are studied qualitatively. It is shown that in the Lagrange integrable case, the trajectories of solutions starting at the boundary of a possible motion area can both cover and not cover the entire possible motion area. Contrary to this is the case of the systems without gyroscopic forces, where the trajectories always cover the possible motion area. For the Kovalevskaya top the possible motion area can both be covered and not covered by the trajectories.
##### MSC:
 7e+18 Motion of a rigid body with a fixed point
##### Keywords:
gyroscopic forces; Lagrange top; Kovalevskaya top
Full Text:
##### References:
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