Invariant polygons in systems with grazing-sliding

Chaos

Volumn 18, Issue 2, 2008, Pages

  Szalai, R ^a   Osinga, H M ^a  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 46449116815     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2904774     Document Type: Article

References (28)

1. P. Armstrong-H́louvry, P. DuPont, and C. C. de Wit, " A survey of models, analysis tools and compensation methods for the control of machines with friction.," Automatica 30, 1083-1138 (1994).
2. D. K. Campbell, R. Galeeva, and C. Tresser, " Piecewise linear models for the quasiperiodic transition to chaos.," Chaos 6, 121-154 (1996).
3. P. Casini, O. Giannini, and F. Vestroni, " Experimental evidence of non-standard bifurcations in non-smooth oscillator dynamics.," Nonlinear Dyn. 46, 259-272 (2006).
4. G. Csernák and G. St́pán, " On the periodic response of a harmonically excited dry friction oscillator.," J. Sound Vib. 295, 649-658 (2006).
5. H. Dankowicz, P. Piiroinen, and A. B. Nordmark, " Low-velocity impacts of quasiperiodic oscillations.," Chaos, Solitons Fractals 14, 241-255 (2002).
6. M. di Bernardo, C. J. Budd, A. R. Champneys, and P. Kowalczyk, Bifurcation and Chaos in Piecewise-smooth Dynamical Systems: Theory and Applications (Springer, Berlin, 2007).
7. M. di Bernardo, P. Kowalczyk, and A. Nordmark, " Sliding bifurcations: A novel mechanism for sudden onset of chaos in dry friction oscillators.," Int. J. Bifurcation Chaos Appl. Sci. Eng. 13, 2935-2948 (2003).
8. B. Feeny and F. C. Moon, " Chaos in a forced dry friction oscillator: Experiments and numerical modelling.," J. Sound Vib. 170, 303-323 (1994).
9. A. F. Filippov, Differential Equations with Discontinuous Right-Hand Sides (Kluwer, Dordrecht, 1988).
10. S. J. Hogan, L. Higham, and T. C. L. Griffin, " Dynamics of a piecewise linear map with a gap.," Proc. R. Soc. London, Ser. A 463, 49-65 (2007).
11. A. J. Homburg, " Piecewise smooth interval maps with non-vanishing derivative.," Ergod. Theory Dyn. Syst. 20, 749-773 (2000).
12. A. C. J. Luo and B. C. Gegg, " Stick and non-stick periodic motions in periodically forced oscillators with dry friction.," J. Sound Vib. 291, 132-168 (2006).
13. J. Moser, Stable and Random Motions in Dynamical Systems (Princeton University Press, Princeton, 1973).
14. S. Narayanan and K. Jayaraman, " Chaotic vibration in a nonlinear oscillator with Coulomb damping.," J. Sound Vib. 146, 17-31 (1991).
15. A. B. Nordmark, " Nonperiodic motion caused by grazing incidence in an impact oscillator.," J. Sound Vib. 145, 279-297 (1991).
16. B. Novák, Z. Pataki, A. Ciliberto, and J. J. Tyson, " Mathematical model of the cell division cycle of fission yeast.," Chaos 11, 277-286 (2001).
17. J. Nussbaum and A. Ruina, " A two degree-of-freedom earthquake model with static/dynamic friction.," Pure Appl. Geophys. 125, 629-656 (1987).
18. M. Oestreich, N. Hinrichs, and K. Popp, " Bifurcation and stability analysis for a nonsmooth friction oscillator.," Arch. Appl. Mech. 66, 301-314 (1996).
19. P. T. Piiroinen and Y. A. Kuznetsov, " An event-driven method to simulate Filippov systems with accurate computing of sliding motions.," ACM Trans. Math. Softw. (to be published).
20. K. Popp and P. Stelter, " Stick-slip vibration and chaos.," Philos. Trans. R. Soc. London 332, 89-105 (1990).
21. J. Sieber, P. Kowalczyk, S. J. Hogan, and M. di Bernardo, " Dynamics of symmetric hybrid dynamical systems with delay. " (special issue), preprint, pages 1-29, 2007, http://www.abdn.ac.uk/~eng824/documents/SKHD07.pdf
22. R. Stribeck, " Die wesentlischen Eigenschaften der Gleit- und Rollenlager.," Zeitschrift des Vereines deutscher Ingenieure (pt I) 46, 1341-1348 (1902); R. Stribeck, " Die wesentlischen Eigenschaften der Gleit- und Rollenlager.," Zeitschrift des Vereines deutscher Ingenieure (pt II) 46, 1432-1438 (1902); R. Stribeck, " Die wesentlischen Eigenschaften der Gleit- und Rollenlager.," Zeitschrift des Vereines deutscher Ingenieure (pt III) 46, 1463-1470 (1902).
23. I. Sushko, T. Puu, and L. Gradini, The Hicksian floor-roof model for two regions linked by interregional trade, Chaos., Chaos, Solitons Fractals 18, 593-612 (2003).
24. P. Thota and H. Dankowicz, " Continuous and discontinuous grazing bifurcations in impacting oscillators.," Physica D 214, 187-197 (2005).
25. V. I. Utkin, Sliding Modes in Control and Optimization (Springer, Berlin, 1992).
26. S. Wiggins, Global Bifurcations and Chaos (Springer, Berlin, 1988).
27. Z. T. Zhusubaliyev and E. Mosekilde, " Torus birth bifurcations in a DC/DC converter.," IEEE Trans. Circuits Syst., I: Regul. Pap. 53, 1839-1850 (2006).
28. Z. T. Zhusubaliyev, E. Mosekilde, S. Maity, S. Mohanan, and S. Banerjee, " Border collision route to quasiperiodicity: Numerical investigation and experimental confirmation.," Chaos 16, 023122 (2006).