SOLVING THE PROBLEM OF STABILIZATION OF A GYROSCOPIC SYSTEM WITH THE HELP
                  OF COMPUTER ALGEBRA.
     A.V. Banshchikov, L.A. Bourlakova, V.D. Irtegov
    (Institute of Systems Dynamics and Control Theory SB RAS
        134, Lermontov St., Irkutsk, 664033, Russia
            E-mail : irteg@icc.ru )

There is a classic problem of stabilization of a potential system with
even order of instability by gyroscopic forces. Such systems are critical
in Lyapunov sense, thus we use second method of stability theory.
Important subproblem is obtaining sufficient conditions of stabilization
which are close to necessary conditions.
In the report we discuss (i) methods of constructing effective Lyapunov
functions, (ii) problems of investigation of sign-definitiveness of the
forms, (iii) parametric analysis of conditions of stabilization,
(iv) influence of nonlinear forces.  Algorithms use abilities of
computer algebra.  Report contains examples.

Keywords:  Lyapunov functions, potential systems, gyroscopic forces,
second method of stability theory, computer algebra.