An Analytical Approach to Codimension-2 Sliding Bifurcations in the Dry-Friction Oscillator

In this paper, we consider analytically sliding bifurcations of periodic orbits in the dry friction oscillator. The system depends on two parameters; F , which corresponds to the intensity of the friction and ω, the frequency of the forcing. We prove the existence of infinitely many codimension-2 bifurcation points and we focus our attention on two of them; A1 := (ω , F ) = (2, 1/3) and B1 := (ω, F ) = (3, 0). We derive analytic expressions in (ω, F ) parameter space for the codimension-1 bifurcation curves that emanate from A1 and B1. We show excellent agreement with the numerical calculations of Kowalczyk and Piiroinen [KP08].