This book presents the theoretical frame for studying lumped nonsmooth dynamical systems: the mathematical methods are recalled, and adapted numerical methods are introduced (differential inclusions, maximal monotone operators, Filippov theory, Aizerman theory, etc.). Tools available for the analysis of classical smooth nonlinear dynamics (stability analysis, the Melnikov method, bifurcation scenarios, numerical integrators, solvers, etc.) are extended to the nonsmooth frame. Many models and applications arising from mechanical engineering, electrical circuits, material behavior and civil engineering are investigated to illustrate theoretical and computational developments.
Contents:
- Introduction to Discontinuous ODEs
- Mathematical Background for Multivalued Formulations
- Properties of Numerical Schemes
- Stick–Slip Oscillator with Two Degrees of Freedom
- Piecewise Linear Approximations
- Chua's Circuit with Discontinuities
- One DOF Mechanical System with Friction
- A Mechanical System with 7 DOF
- Triple Pendulum with Impacts
- Analytical Prediction of Stick–Slip Chaos
- and other topics
Readership: Upper-level undergraduates, graduate students, researchers and practitioners in engineering mechanics, civil engineering, biomechanics, and nonlinear sciences and applications.
