Lyapunov exponents and coexistence of attractors in vibro-impact systems with symmetric two-sided rigid constraints

A three-degree-of-freedom vibro-impact system with symmetric two-sided rigid constraints is considered. The six-dimensional Poincaré map can be expressed as the second iteration of another unsymmetric implicit map. Based on the QR method, the unsymmetric implicit map is used to calculate all the Lyapunov exponents. The calculation method can be applied for other vibro-impact systems with symmetric two-sided rigid constraints. By numerical simulations, the attractors are represented in the projected Poincaré section, and are characterized by the Lyapunov exponents. It is shown that the coexistence of attractors is frequent in the system.