Computer algebra and problems of motion stability

The paper discusses algorithms for investigation of the stability of mechanical systems: (i) investigation of stability in the first approximation; (ii) Algorithms for constructing Lyapunov functions. A special attention is given to the cases critical in the Lyapunov sense; (iii) algorithms intended for application of theorems of Lyapunov’s second method to investigation of stability of complex mechanical systems which assume decomposition. As an example, a problem of the stability of an orbited satellite with an active gravitational stabilizer is considered.