Abstract
A gyrostat [1] is a mechanical system S which consists of a solid body S 1 and other bodies S 2 which are connected to it. These other bodies are either variable or solid, but their motion relative to the body S 1 does not alter the geometry of the mass system S. Examples of such systems are: a solid body to which there are connected axes of several (or of one) symmetric gyroscopes: or a solid body with a cavity of arbitrary shape entirely filled with a homogeneous liquid; and similar systems. It is obvious that for a given distribution of masses in a gyrostat no change can occur in the position of the center of gravity of the principal axes and of the moments of inertia of the gyrostat with respect to any point of the solid body S 1 as the result of the internal motion of the bodies S 2. In the present work there is investigated, by the use of the second method of Liapunov, the stability of certain motions of heavy gyrostats with one fixed point.
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