Periodic orbits of an impact oscillator
An harmonically excited, undamped linear oscillator with impacts is considered. The structure of the orbit space for single-excitation-cycle, singleimpact periodic orbits is investigated, first for elastic and then for inelastic impacts. It is proved that these orbits form a smooth, connected threedimensional manifold in the five-dimensional global parameter space. A study of the dynamic stability of these orbits then shows that the linearly stable region occupies an open submanifold. Numerically generated diagrams representing projections of the orbit spaces for a range of restitution coefficients are included. In addition, the impact surface — a representation in phase space of the impact obstacle — is explored and some new results on its variation with respect to the position of the obstacle are presented.