Active orientation of a gyrostat with variable moments of inertia

The problem of the uniaxial and triaxial orientation of a balanced gyrostat with time-dependent moments of inertia relative to König and non-inertial systems of coordinates is considered. An active stabilizing control is constructed analytically in a class of continuous functions according to a feedback principle, and the conditions under which a desirable orientation that has the property of asymptotic stability is possible are determined. The method of Lyapunov functions and the method of limit equations and limit systems, which enables Lyapunov functions with sign-constant derivatives to be employed, are used. An example of the numerical simulation of the triaxial orientation of a gyrostat is presented.