Modeling, Analysis and Control of Dynamical Systems

With Friction and Impacts

By: Pawel Olejnik, Jan Awrejcewicz, Michal Feckan

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eText | 7 July 2017

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This book is aimed primarily towards physicists and mechanical engineers specializing in modeling, analysis, and control of discontinuous systems with friction and impacts. It fills a gap in the existing literature by offering an original contribution to the field of discontinuous mechanical systems based on mathematical and numerical modeling as well as the control of such systems. Each chapter provides the reader with both the theoretical background and results of verified and useful computations, including solutions of the problems of modeling and application of friction laws in numerical computations, results from finding and analyzing impact solutions, the analysis and control of dynamical systems with discontinuities, etc. The contents offer a smooth correspondence between science and engineering and will allow the reader to discover new ideas. Also emphasized is the unity of diverse branches of physics and mathematics towards understanding complex piecewise-smooth dynamical systems. Mathematical models presented will be important in numerical experiments, experimental measurements, and optimization problems found in applied mechanics.

Contents:

Friction Laws in Modeling of Dynamical Systems
Transient Friction-Induced Vibrations in a 2-DOF Braking System
Numerical Estimation of the Stick-Slip Transitions
Smooth Approximation of Discontinuous Stick-Slip Solutions
Bifurcations in Planar Discontinuous Systems
Occurrence of Chaos in Forced Impact Systems
Impacts in Chaotic Motion of a Particle on a Non-Flat Billiard
Parameter Identification of a Double Torsion Pendulum with Friction
Identification of Time-Varying Damping of a Parametric Pendulum with Friction
Almost Periodic Solutions for Jumping Discontinuous Systems
Solution of Nonlinear Algebraic Equations in Analysis of Stability
Control of a Wheeled Double Inverted Pendulum with Friction
Tracking Control of a Discontinuous System with Stick-Slip Friction
Control of Stochastically Excited Systems with an Approximate Discontinuity

Readership: Physicists and mechanical engineers specializing in modeling, analysis and control of discontinuous systems.
Friction Laws;Friction-Induced Vibrations;Creep-Slip;Stick-Slip;Discontinuous Systems;Filippov-Type Systems;Jumping Discontinuous Systems;Impacts;Melnikov Function;Asymmetric Pendulum;System Modeling;Mechatronic Systems;Mechanical Models;Periodic Solutions;Chaotic Solutions;Homoclinic Solutions;Numerical Solutions;Parameter Identification;Discontinuity Approximation;Optimization;Control of Dynamical Systems;Stability Analysis;Dynamical Analysis;Bifurcation Analysis;Experimental MeasurementsKey Features:

Mathematical theories developed here and presented focus on classical mechanics explained in a modern way
Verified results of the application of dedicated computational methods
Provides a unique theoretical background for investigating special mechanical systems with discontinuities, presenting their dynamical analysis, optimization and control
Many original problems of physics of a solid body, mathematical analysis, and mechanical engineering are investigated