Abstract
A geometrical interpretation is proposed of the stability conditions for steady solutions of dynamical systems with simple symmetry in the Lyapunov-critiatl case, i.e. when the matrix of the linearization has one zero eigenvalue and all other eigenvalues have negative real parts. The change in the nature of the stability of a singular point when the parameter is varied is associated with bifurcations, represented by cusp and butterfly singularities of the manifolds of steady states. Analytic and numerical constructions are given of the bifurcation sets of the two-parameter families of steady states of two-unit systems with rolling, and the relationship of the system parameters responsible for the unsafe-safe boundary of the stability domain is determined.
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