Abstract: 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 subharmonic motions is deduced based on the Poincaré map method and the oblique impact relations with non-fixed impact positions. The stability of these subharmonic periodic motions is analyzed by the Floquet theory, and the formulas to calculate the Floquet 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 non-fixed impact positions is analyzed.

Key words: impact with non-fixed position, oblique impact, subharmonic motion, existence, stability, probability distribution