Dynamic analysis of two-degree-of-freedom oblique impact system with non-fixed impact positions

The dynamic behavior of a two-degree-of-freedom oblique impact system consisted of two pendulums with non-fixed impact positions is investigated. The relations between the restitution coefficient, the friction coefficient, as well as other parameters of the system and the states before or after impact, are clarified in this oblique impact process. The existence criterion of single impact periodic-n subharrnonic motions is deduced based on the Poincare map method and the oblique impact relations with non-fixed impact positions. The stability of these subharrnonic periodic motions is analyzed by the Floquet theory, and the formulas to calculate the Flocluet multipliers are given. The validity of this method is shown through numerical simulation. At the same time, the probability distribution of impact positions in this oblique system with nonfixed impact positions is analyzed.