## Chaotic Mechanics in Systems with Impacts and FrictionThis book is devoted to the theory of chaotic oscillations in mechanical systems. Detailed descriptions of the basic types of nonlinearity ? impacts and dry friction ? are presented. The properties of such behavior are discussed, and the numerical and experimental results obtained by the authors are presented.The dynamic properties of systems described here can be useful in the proper design and use of mechanics where such behavior still creates problems.This book will be very useful for anyone with a fundamental knowledge of nonlinear mechanics who is beginning research in the field. |

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### Contents

Preface | 1 |

Impact oscillator with dry friction | 75 |

Systems with impacts | 113 |

Systems with friction | 141 |

161 | |

164 | |

Nonlinear Dynamics Chaos in Mechanical Systems with Discontinuities | 173 |

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### Common terms and phrases

amplitude analysis angular velocity bifurcation diagram Blazejczyk bodies boundary cantilever beam changes chaos chaotic attractor chaotic behavior chaotic motion characteristics circle map coefficient of restitution correlation dimension damping coefficient deformation degrees of freedom denotes described Devil's attractors Devil's staircase dimension dynamics elastic equation of motion equilibrium position example exciting force experimental Feigenbaum fender Figure forced vibrations friction force function grazing impact harmonic impact damper impact force impact occurs impact oscillator intermittency investigations Isomaki Kapitaniak limit cycle linear Lyapunov dimension Lyapunov exponents map of impacts mass m2 mechanical system Melnikov method nonlinear Nordmark numerical observed obtained Omega pendulum period doubling periodic impact motion periodic motion Peterka phenomena phenomenon Poincare map power spectra presented properties quasi-periodic motion relative velocity restitution coefficients rotor shown in Fig shows simulation spheres subharmonic subsystem surfaces system motion system parameters system with impacts systems with dry Wojewoda