On the stationary motions of a rigid body with a spherical support

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Abstract

We conduct the qualitative analysis of differential equations describing the rotation of a dynamically asymmetric rigid body around a fixed point. The body is enclosed in a spherical shell, to which one ball and one disk adjoin. The motion of the body by inertia and under the action of potential forces is considered. It is established that in the absence of external forces, the differential equations have the families of solutions corresponding to the equilibrium positions of the body, and in the case of potential forces there exist manifolds of pendulum motions. For a number of the solutions, the necessary and sufficient conditions of the Lyapunov stability are derived.

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About the authors

V. D. Irtegov

Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences

Author for correspondence.
Email: irteg@icc.ru
Russian Federation, Irkutsk

T. N. Titorenko

Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences

Email: titor@icc.ru
Russian Federation, Irkutsk

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