Abstract
In this paper, we analytically consider 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 $\omega$, the frequency of the forcing. We prove the existence of infinitely many codimension-2 bifurcation points and focus our attention on two of them: $A_1:=(\omega\ii, F)=(2, 1/3)$ and $B_1:=(\omega\ii, F)=(3,0)$. We derive analytic expressions in ($\omega\ii$, $F$) parameter space for the codimension-1 bifurcation curves that emanate from $A_1$ and $B_1$. Our results show excellent agreement with the numerical calculations of Kowalczyk and Piiroinen.
Translated title of the contribution | An analytical approach to codimension-2 sliding bifurcations in the dry friction oscillator |
---|---|
Original language | English |
Pages (from-to) | 769 - 798 |
Number of pages | 29 |
Journal | SIAM Journal on Applied Dynamical Systems |
Volume | 9 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2010 |
Research Groups and Themes
- Engineering Mathematics Research Group