{"product_id":"vibro-impact-dynamics-hardback-9781118359457","title":"Vibro-impact Dynamics (Hardback) 9781118359457","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eVibro-impact Dynamics\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eAlbert C. J. Luo (Author), Yu Guo (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781118359457, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 18 January 2013\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e272 pages\u003cbr\u003e25.2 x 17.5 x 1.8 cm, 0.558 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e\"It provides a unified treatment on the topic with a sound theoretical base that is applicable to both continuous and discrete systems.\" (Zentralblatt MATH, 2016)    \u003cbr\u003e\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e\u003cb\u003ePresents a systematic view of vibro-impact dynamics based on the nonlinear dynamics analysis\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eComprehensive understanding of any vibro-impact system is critically impeded by the lack of analytical tools viable for properly characterizing grazing bifurcation. The authors establish vibro-impact dynamics as a subset of the theory of discontinuous systems, thus enabling all vibro-impact systems to be explored and characterized for applications. \u003c\/p\u003e \u003cp\u003e\u003ci\u003eVibro-impact Dynamics\u003c\/i\u003e presents an original theoretical way of analyzing the behavior of vibro-impact dynamics that can be extended to discontinuous dynamics. All topics are logically integrated to allow for vibro-impact dynamics, the central theme, to be presented. It provides a unified treatment on the topic with a sound theoretical base that is applicable to both continuous and discrete systems\u003c\/p\u003e \u003cp\u003e\u003ci\u003eVibro-impact Dynamics:\u003c\/i\u003e\u003c\/p\u003e \u003cul\u003e \u003cli\u003ePresents mapping dynamics to determine bifurcation and chaos in vibro-impact systems\u003c\/li\u003e \u003cli\u003eOffers two simple vibro-impact systems with comprehensive physical interpretation of complex motions\u003c\/li\u003e \u003cli\u003eUses the theory for discontinuous dynamical systems on time-varying domains, to investigate the Fermi-oscillator\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eEssential reading for graduate students, university professors, researchers and scientists in mechanical engineering.\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003ePreface ix\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Discrete and Discontinuous Systems 1\u003c\/p\u003e \u003cp\u003e1.1.1 Discrete Dynamical Systems 1\u003c\/p\u003e \u003cp\u003e1.1.2 Discontinuous Dynamical Systems 4\u003c\/p\u003e \u003cp\u003e1.2 Fermi Oscillators and Impact Problems 7\u003c\/p\u003e \u003cp\u003e1.3 Book Layout 9\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Nonlinear Discrete Systems 11\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Definitions 11\u003c\/p\u003e \u003cp\u003e2.2 Fixed Points and Stability 13\u003c\/p\u003e \u003cp\u003e2.3 Stability Switching Theory 22\u003c\/p\u003e \u003cp\u003e2.4 Bifurcation Theory 38\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Complete Dynamics and Fractality 47\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Complete Dynamics of Discrete Systems 47\u003c\/p\u003e \u003cp\u003e3.2 Routes to Chaos 54\u003c\/p\u003e \u003cp\u003e3.2.1 One-Dimensional Maps 54\u003c\/p\u003e \u003cp\u003e3.2.2 Two-Dimensional Systems 58\u003c\/p\u003e \u003cp\u003e3.3 Complete Dynamics of the Henon Map 59\u003c\/p\u003e \u003cp\u003e3.4 Similarity and Multifractals 64\u003c\/p\u003e \u003cp\u003e3.4.1 Similar Structures in Period Doubling 65\u003c\/p\u003e \u003cp\u003e3.4.2 Fractality of Chaos via PD Bifurcation 68\u003c\/p\u003e \u003cp\u003e3.4.3 An Example 70\u003c\/p\u003e \u003cp\u003e3.5 Complete Dynamics of Logistic Map 72\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Discontinuous Dynamical Systems 85\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Basic Concepts 85\u003c\/p\u003e \u003cp\u003e4.2 G-Functions 88\u003c\/p\u003e \u003cp\u003e4.3 Passable Flows 91\u003c\/p\u003e \u003cp\u003e4.4 Non-Passable Flows 95\u003c\/p\u003e \u003cp\u003e4.5 Grazing Flows 107\u003c\/p\u003e \u003cp\u003e4.6 Flow Switching Bifurcations 119\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Nonlinear Dynamics of Bouncing Balls 131\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Analytic Dynamics of Bouncing Balls 131\u003c\/p\u003e \u003cp\u003e5.1.1 Periodic Motions 133\u003c\/p\u003e \u003cp\u003e5.1.2 Stability and Bifurcation 136\u003c\/p\u003e \u003cp\u003e5.1.3 Numerical Illustrations 140\u003c\/p\u003e \u003cp\u003e5.2 Period-m Motions 143\u003c\/p\u003e \u003cp\u003e5.3 Complex Dynamics 152\u003c\/p\u003e \u003cp\u003e5.4 Complex Periodic Motions 156\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Complex Dynamics of Impact Pairs 165\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Impact Pairs 165\u003c\/p\u003e \u003cp\u003e6.2 Analytical, Simplest Periodic Motions 168\u003c\/p\u003e \u003cp\u003e6.2.1 Asymmetric Period-1 Motion 170\u003c\/p\u003e \u003cp\u003e6.2.2 Stability and Bifurcation 172\u003c\/p\u003e \u003cp\u003e6.2.3 Numerical Illustrations 175\u003c\/p\u003e \u003cp\u003e6.3 Possible Impact Motion Sequences 179\u003c\/p\u003e \u003cp\u003e6.4 Grazing Dynamics and Stick Motions 182\u003c\/p\u003e \u003cp\u003e6.5 Mapping Structures and Periodic Motions 189\u003c\/p\u003e \u003cp\u003e6.6 Stability and Bifurcation 192\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Nonlinear Dynamics of Fermi Oscillators 203\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Mapping Dynamics 203\u003c\/p\u003e \u003cp\u003e7.2 A Fermi Oscillator 209\u003c\/p\u003e \u003cp\u003e7.2.1 Absolute Description 210\u003c\/p\u003e \u003cp\u003e7.2.2 Relative Description 212\u003c\/p\u003e \u003cp\u003e7.3 Analytical Conditions 214\u003c\/p\u003e \u003cp\u003e7.4 Mapping Structures and Motions 218\u003c\/p\u003e \u003cp\u003e7.4.1 Switching Sets and Generic Mappings 218\u003c\/p\u003e \u003cp\u003e7.4.2 Motions with Mapping Structures 221\u003c\/p\u003e \u003cp\u003e7.4.3 Periodic Motions and Local Stability 223\u003c\/p\u003e \u003cp\u003e7.5 Predictions and Simulations 226\u003c\/p\u003e \u003cp\u003e7.5.1 Bifurcation Scenario 226\u003c\/p\u003e \u003cp\u003e7.5.2 Analytical Prediction 229\u003c\/p\u003e \u003cp\u003e7.5.3 Numerical Simulations 236\u003c\/p\u003e \u003cp\u003eAppendix 7.A 248\u003c\/p\u003e \u003cp\u003eReferences 253\u003c\/p\u003e \u003cp\u003eIndex 259\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mechanical engineering \u0026amp; materials [\u003ca title=\"See our other books on Mechanical engineering \u0026amp; materials\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mechanical%20engineering%20\u0026amp;%20materials%20%5BTG%5D%22\"\u003eTG\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Wiley","offers":[{"title":"Brand 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