On a class of motions of a Zhukovskii gyrostat with variable gyrostatic moment

Abstract

The paper deals with the problem of Zhukovskii gyrostat motions in the case of a constant angle between the gyrostat invariable axis and the gyrostat angular momentum vector. It is assumed that the gyrostatic moment depends on time. The obtained conditions on the gyrostat parameters and the expression for the gyrostatic moment characterize a new solution of the Zhukovskii equations with variable gyrostatic moment. We prove that it describes semiregular precession of the first type with respect to the angular momentum vector.