Chaos in a simple impact oscillator

摘要

In this study dynamics of a forced impact oscillator is investigated. The equations of systems were derived and solved analytically. Different dynamical regimes including periodic and chaotic were observed. Period doubling bifurcation was detected analytically by calculating the critical values of the eigenvalues of the Jacobian matrix. Lyapunov exponents were calculated by a modern method utilizing the poincare map and its accuracy was proved by comparison with bifurcation diagram. Finally fractal dimension was computed for chaotic attractors that verified their strange nature.