Cg. Gibson et Ca. Hobbs, SINGULARITIES OF GENERAL ONE-DIMENSIONAL MOTIONS OF THE PLANE AND SPACE, Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, 125, 1995, pp. 639-656
Local models are given for the singularities which can appear on the t
rajectories of general one-dimensional motions of the plane or space.
Versal unfoldings of these model singularities give simple pictures de
scribing the family of trajectories arising from small deformations of
the tracing point.