REAL BIFURCATIONS OF 2-UNIT SYSTEMS WITH ROLLING

A geometrical interpretation is proposed of the stability conditions f or steady solutions of dynamical systems with simple symmetry in the L yapunov-critical case, i.e. when the matrix of the linearization has o ne zero eigenvalue and all other eigenvalues have negative real parts. The change in the nature of the stability of a singular point when th e parameter is varied is associated with bifurcations, represented by cusp and butterfly singularities of the manifolds of steady states. An alytic and numerical constructions are given of the bifurcation sets o f the two-parameter families of steady states of two-unit systems with rolling, and the relationship of the system parameters responsible fo r the unsafe-safe boundary of the stability domain is determined. Copy right (C) 1996 Elsevier Science Ltd.