On one approach to the qualitative analysis of nonlinear dynamical systems

By an example of the investigation of the Euler equations on Lie algebras, we discuss an approach to the qualitative analysis of differential equations arising in a number of problems of mathematical physics, including rigid body dynamics. The approach proposed is based on a combination of methods of computer algebra and qualitative analysis of differential equations. We consider the applications of computer algebra in the problems of finding stationary invariant sets and studying their stability. For the equations under study, stationary invariant sets of various dimension have been found and their stability in the Lyapunov sense has been investigated.