BIFURCATIONS OF STEADY-STATES IN SYSTEMS WITH ROLLING UNDER CONSTANT FORCE PERTURBATIONS

Mechanical systems in which the interaction of a rolling elastic body with the supporting plane can be described by well-known axioms [1] ar e studied. When there are no external forces they belong to dynamical systems with symmetry [2]. A sideways force applied at the centre of m ass and the moment of forces about the vertical axis are regarded as s ymmetry defects. The bifurcation sets of two-, three-, and four-parame ter families of steady states are analysed. A procedure for constructi ng the explicit or parametric forms of the bifurcation surface without constructing the set of steady states is proposed. It is shown that f or different values of the control parameters the bifurcation set can have singularities, which can be classified as the cusp, swallow tail, and butterfly catastrophes [3].