Abstract
In this chapter, two dynamical systems connected with frictions will be presented, and such two discontinuous dynamical systems possess a moving boundary. For such a problem, the analytical conditions for motion switching and sliding on the time-varying boundary will be developed. Based on the time-varying boundary, the basic mappings are introduced and the mapping structures for periodic motions will be developed. From a certain mapping structure, the corresponding periodic motions will be predicted analytically and the corresponding local stability and bifurcation analysis will be completed. To understand the singularity and switchability of motions to the time-varying boundary in such a two-mass system, illustrations of periodic motions will be given from analytical predictions. The relative forces will be presented for illustration of the analytical conditions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Luo, A. C. J. (2005a), A theory for non-smooth dynamical systems on connectable domains, Communication in Nonlinear Science and Numerical Simulation, 10, pp. 1–55.
Luo, A. C. J. (2005b), Imaginary, sink and source flows in the vicinity of the separatrix of non-smooth dynamic systems, Journal of Sound and Vibration, 285, pp. 443–456.
Luo, A. C. J. (2007a), Differential geometry of flows in nonlinear dynamical systems, Proceedings of IDECT’07, ASME International Design Engineering Technical Conferences, September 4–7, 2007, Las Vegas, Nevada, USA. DETC2007-84754.
Luo, A. C. J. (2007b), On flow switching bifurcations in discontinuous dynamical system, Communications in Nonlinear Science and Numerical Simulation, 12, pp. 100–116.
Luo, A. C. J. (2008a), A theory for flow switchability in discontinuous dynamical systems, Nonlinear Analysis: Hybrid Systems, 2, pp. 1030–1061.
Luo, A. C. J. (2008b), Global Transversality, Resonance and Chaotic Dynamics, Singapore: World Scientific.
Luo, A. C. J. and Thapa, S. (2007), On nonlinear dynamics of simplified brake dynamical systems, Proceedings of IMECE2007, 2007 ASME International Mechanical Engineering Congress and Exposition, November 5–10, 2007. Scattle, Washington, USA. IMECE2007-42349.
Luo, A. C. J. and Thapa, S. (2009), Periodic motion in a simplified brake system with a periodic excitation, Communication in Nonlinear Science and Numerical Simulation, 14, pp. 2389–2414.
Rights and permissions
Copyright information
© 2009 Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
(2009). Dynamical Systems with Frictions. In: Discontinuous Dynamical Systems on Time-varying Domains. Nonlinear Physical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00253-3_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-00253-3_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00252-6
Online ISBN: 978-3-642-00253-3
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)