Modeling, Analysis And Control Of Dynamical Systems With Friction And Impacts

Modeling, Analysis And Control Of Dynamical Systems With Friction And Impacts

With Friction and Impacts

Paweł Olejnik, Jan Awrejcewicz;Michal Fečkan;;


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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.

  • 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