Qualitative Analysis of Nonsmooth Dynamics

Qualitative Analysis of Nonsmooth Dynamics: A Simple Discrete System with Unilateral Contact and Coulomb Friction explores the effects of small and large deformations to understand how shocks, sliding, and stick phases affect the trajectories of mechanical systems. By analyzing these non-regularities successively this work explores the set of equilibria and properties of periodic solutions of elementary mechanical systems, where no classical results issued from the theory of ordinary differential equations are readily available, such as stability, continuation or approximation of solutions. The authors focus on unilateral contact in presence of Coulomb friction and show, in particular, how any regularization would greatly simplify the mathematics but lead to unacceptable physical responses.

• Explores the effects of small and large deformations to understand how shocks, sliding, and stick phases affect the trajectories of mechanical systems
• Includes theoretical results concerning the full investigation of the behavior under constant or oscillating loadings, even in the case of the simplest mechanical systems
• Provides a focus on unilateral contact in presence of Coulomb friction
• Helps you gain an accurate understanding of how the transition occurs to ensure the safe use of any machine involving rotating or sliding mechanisms

PhD students, researchers, academics and engineers in the field of mechanical engineering

Introduction
Chapter 1. The Model
Chapter 2. Mathematical Formulation
Chapter 3. The Equilibrium States
Chapter 4. Stability
Chapter 5. Exploring the Case of the Linear Restoring Force
Chapter 6. The Case of the Nonlinear Restoring Force
Chapter 7. Open Problems and Challenges