On stability of stationary solutions motion equations of the Goryachev-Sretensky gyrostat with a nonlinear potential

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Abstract

The equations of rotational motion of a gyrostat are studied. The gyrostat is considered under the Goryachev—Sretensky conditions in the case of a nonlinear potential, the derivative of which has real roots with a modulus of no more than one. Parametric families of stationary solutions are found, including states of equilibrium and permanent rotations. Sufficient conditions for the stability of stationary solutions are obtained by the method of Chetaev's integral bundles. Based on the analysis of the roots of the characteristic equation, the conditions for instability are obtained.

About the authors

A. A. Kosov

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

Email: kosov_idstu@mail.ru
Irkutsk, Russia

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