A stability analysis method for Period-1 solution in Two-Mass impact oscillator

Abstract

In this paper, we propose a stability analysis method for the period-1 solution in two-mass impact oscillators. First, we describe a dynamical model and its solution. Next, we define the Poincaré map and then we derive derivative of the Poincaré map. In particular, we explain the elements of the Jacobian matrix to perform the stability analysis numerically. Finally, we apply this method to a simple two-mass impact oscillator and confirm its validity.