Catastrophe Theory and the Vibro-impact Dynamics of Autonomous Oscillators

Abstract

Non-differentiability in vibro-impact dynamics can lead to breakdown of the global stable manifold theorem, the shredding of stable manifolds and to the generation of homoclinic tangles by the translation of segments of stable and unstable manifolds across each other. This article discusses the non-differentiability of autonomous vibro-impact systems using the methods of catastrophe theory. The singularities are characterised by a hypersurface unfolding the classic singularities such as the cusp and the swallowtail.