Euler equations on Lie algebras are used, as an example, to discuss an approach to qualitative analysis of differential equations in some problems of mathematical physics, including rigid body dynamics. The approach is based on a combination of methods of computer algebra and qualitative analysis of differential equations. Applications of computer algebra in problems of finding stationary invariant sets and studying their stability are considered. For the above equations, stationary invariant sets of various dimensions are found and their Lyapunov stability is investigated.
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