A class of three invariant relations for the equations of motion of a gyrostat with a variable gyrostatic moment

The motion of a dynamically symmetrical gyrostat under the action of potential and gyroscopic forces with a variable gyrostatic moment, which can be described by generalized equations of the Kirchhoff–Poisson class, is considered. The conditions for the existence of three linear invariant relations of a special type are obtained, and new solutions of the equations of motion, expressed either in the form of elementary functions or elliptic functions of time, are obtained. ©2013