Analytical drift reconstruction for visco-elastic impact oscillators operating in periodic and chaotic regimes

An impact oscillator with a drift, which is important in many applications, is considered. The model accounts for the visco-elastic impacts and is capable to mimic the dynamics of a bounded progressive motion. To simplify the dynamic analysis a simple transformation decoupling the original co-ordinates is proposed. As the result the bounded oscillations can be studied separately from the drift as the drift does not influence the dynamics of the bounded system. On the contrary the drift depends on the bounded dynamics and can be reconstructed once the bounded oscillatory motion is determined. The accuracy of the analytical reconstruction allows to calculate even strange chaotic attractors. Evolutions of co-existing periodic and strange attractors were studied.