Discontinuous Dynamical Systems on Time-varying Domains is the first monograph focusing on this topic. While in the classic theory of dynamical systems the focus is on dynamical systems on time-invariant domains， this book presents discontinuous dynamical systems on time-varying domains where the corresponding switchability of a flow to the time-varying boundary in discontinuous dynamical systems is discussed. From such a theory， principles of dynamical system interactions without any physical connections are presented. Several discontinuous systems on time-varying domains are analyzed in detail to show how to apply the theory to practical problems. The book can serve as a reference book for researchers， advanced undergraduate and graduate students in mathematics， physics and mechanics.
- Front Matter
- 1 Introduction
- 1.1 Discontinuous systems
- 1.2 Book layout
- References
- 2 Flow Switchability
- 2.1 Discontinuous dynamic systems
- 2.2 G-functions
- 2.3 Passable flows
- 2.4 Non-passable flows
- 2.5 Tangential flows
- 2.6 Switching bifurcations
- References
- 3 Transversality and Sliding Phenomena
- 3.1 A controlled system
- 3.2 Transversality conditions
- 3.3 Mappings and predictions
- 3.4 Periodic and chaoticmotions
- References
- 4 A Frictional Oscillator on Time-varying Belt
- 4.1 Mechanicalmodel
- 4.2 Analytical conditions
- 4.2.1 Equations ofmotion
- 4.2.2 Passable flows to boundary
- 4.2.3 Sliding flows on boundary
- 4.2.4 Grazing flows to boundary
- 4.3 Generic mappings and force product criteria
- 4.3.1 Genericmappings
- 4.3.2 Sliding flows and fragmentation
- 4.3.3 Grazing flows
- 4.4 Periodicmotions
- 4.4.1 Mapping structures
- 4.4.2 Illustrations
- 4.5 Numerical simulations
- References
- 5 Two Oscillators with Impacts and Stick
- 5.1 Physical problem
- 5.1.1 Introduction to problem
- 5.1.2 Equations ofmotion
- 5.2 Domains and vector fields
- 5.2.1 Absolutemotion description
- 5.2.2 Relativemotion description
- 5.3 Mechanismof stick and grazing
- 5.3.1 Analytical conditions
- 5.3.2 Physical interpretation
- 5.4 Mapping structures andmotions
- 5.4.1 Switching sets and basicmappings
- 5.4.2 Mapping equations
- 5.4.3 Mapping structures
- 5.4.4 Bifurcation scenario
- 5.5 Periodicmotion prediction
- 5.5.1 Approach
- 5.5.2 Impacting chatter
- 5.5.3 Impacting chatterwith stick
- 5.5.4 Parametermaps
- 5.6 Numerical illustrations
- 5.6.1 Impacting chatter
- 5.6.2 Impacting chatterwith stick
- 5.6.3 Further illustrations
- References
- 6 Dynamical Systems with Frictions
- 6.1 Problemstatement
- 6.2 Switching and stick motions
- 6.2.1 Equations ofmotion
- 6.2.2 Analytical conditions
- 6.3 Periodicmotions
- 6.3.1 Switching planes andmappings
- 6.3.2 Mapping structures andmotions
- 6.3.3 Bifurcation scenario
- 6.4 Numerical illustrations
- 6.4.1 Periodic motion without stick
- 6.4.2 Periodicmotionwith stick
- 6.4.3 Periodicmotionwith stick only
- References
- 7 Principles for System Interactions
- 7.1 Two dynamical systems
- 7.1.1 Dynamical systems with interactions
- 7.1.2 Discontinuous description
- 7.1.3 Resultant dynamical systems
- 7.2 Fundamental interactions
- 7.3 Interactions with singularity
- 7.4 Interactions with corner singularity
- References
- Appendix
- A.1 Basic solution
- A.2 Stability and bifurcation
- Index
- 彩图
