Awrejcewicz J., Lamarque C.-H. Bifurcation and Chaos in Nonsmooth Mechanical Systems

World Scientific Publ., 2003. — 563 p. — (World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises 45). — ISBN: 978-238-459-6.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.Introduction to Discontinuous ODEs
Mathematical Background for Multivalued Formulations
Numerical Schemes and Analytical Methods
Properties of Numerical Schemes
Bifurcations of a Particular van der Pol-Duffing Oscillator
Stick-Slip Oscillator with Two Degrees of Freedom
Piecewise Linear Approximations
Chua's Circuit with Discontinuities
Mechanical System with Impacts and Modal Approaches
One DOF Mechanical System with Friction
Modelling the Dynamical Behaviour of Elasto-Plastic Systems
A Mechanical System with 7 DOF
Stability of Singular Periodic Motions in Single Degree
Triple Pendulum with Impacts
Analytical Prediction of Stick-Slip Chaos
Thermoelasticity, Wear and Stick-Slip Movements of a Rotating Shaft with a Rigid Bush
Control for Discrete Models of Buildings Including Elastoplastic Term