{"product_id":"vibroimpact-dynamics-9781118359457","title":"Vibroimpact Dynamics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\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\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\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\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface \u003cp\u003e\u003cb\u003eChapter 1 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 2\u003c\/p\u003e \u003cp\u003e1.1.2 Discontinuous dynamical systems 4\u003c\/p\u003e \u003cp\u003e1.2 Fermi oscillator and impact problems 8\u003c\/p\u003e \u003cp\u003e1.3 book layout 10\u003c\/p\u003e \u003cp\u003eReferences 12\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 2 Nonlinear Discrete Systems 19\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Defintions 19\u003c\/p\u003e \u003cp\u003e2.2 Fixed points and stability 21\u003c\/p\u003e \u003cp\u003e2.3 Stability switching theory 34\u003c\/p\u003e \u003cp\u003e2.4. Bifurcation theory 50\u003c\/p\u003e \u003cp\u003eReferences 59\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 3 Complete Dynamics and Fractality 61\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Complete dynamics of discrete systems 61\u003c\/p\u003e \u003cp\u003e3.2 Routes to chaos 69\u003c\/p\u003e \u003cp\u003e3.2.1 One-dimensional maps 69\u003c\/p\u003e \u003cp\u003e3.2.2 Two-dimensional maps 73\u003c\/p\u003e \u003cp\u003e3.3 Complete Dynamics of Henon map 75\u003c\/p\u003e \u003cp\u003e3.4 Simliarity and Multifractals 81\u003c\/p\u003e \u003cp\u003e3.4.1 Similar Structures in period doubling 81\u003c\/p\u003e \u003cp\u003e3.4.2 Fractality of chaos via PD bifurcation 86\u003c\/p\u003e \u003cp\u003e3.4.3 An example 86\u003c\/p\u003e \u003cp\u003e3.5 Complete dynamics of Logistic map 93\u003c\/p\u003e \u003cp\u003eReferences 107\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 4 Discontinuous Dynamical Systems 109\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Basic concepts 109\u003c\/p\u003e \u003cp\u003e4.2 G-functions 112\u003c\/p\u003e \u003cp\u003e4.3 Passable flows 116\u003c\/p\u003e \u003cp\u003e4.4 Non-passable flows 121\u003c\/p\u003e \u003cp\u003e4.5 Grazing flows 135\u003c\/p\u003e \u003cp\u003e4.6 Flow switching bifucations 149\u003c\/p\u003e \u003cp\u003eReferences 162\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 5 Nonlinear Dynamics of Bouncing Balls 163\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Analytical dynamics of bouncing balls 163\u003c\/p\u003e \u003cp\u003e5.1.1 Periodic motions 165\u003c\/p\u003e \u003cp\u003e5.1.1 Stability and bifurcations 168\u003c\/p\u003e \u003cp\u003e5.1.3 Numerical illustrations 175\u003c\/p\u003e \u003cp\u003e5.2 Period-m motions 180\u003c\/p\u003e \u003cp\u003e5.3 Complex dynamics 187\u003c\/p\u003e \u003cp\u003e5.4 Complex periodic motions 192\u003c\/p\u003e \u003cp\u003eReferences 200\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 6 Complex Dynamics of Impact Pairs 201\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Impact pairs 201\u003c\/p\u003e \u003cp\u003e6.2 Analytical, simplest periodic motions 205\u003c\/p\u003e \u003cp\u003e6.3 Possible impact notion sequences 216\u003c\/p\u003e \u003cp\u003e6.4 Grazing dynamics and stick motions 220\u003c\/p\u003e \u003cp\u003e6.5 Mapping structures and periodic motions 228\u003c\/p\u003e \u003cp\u003e6.6 Stabilityand bifurcation 232\u003c\/p\u003e \u003cp\u003eReferences 242\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 7 Nonlinear Dynamics of Fermi Oscillators 243\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Mapping dynamics 243\u003c\/p\u003e \u003cp\u003e7.2 A Fermi oscillator 249\u003c\/p\u003e \u003cp\u003e7.2.1 Absolute description 251\u003c\/p\u003e \u003cp\u003e7.2.2 Relative description 257\u003c\/p\u003e \u003cp\u003e7.3 Analytical conditions 258\u003c\/p\u003e \u003cp\u003e7.4 Mapping structures and motions 260\u003c\/p\u003e \u003cp\u003e7.4.1 Switching sets and generic mappings 260\u003c\/p\u003e \u003cp\u003e7.4.2 Motions with mapping structures 263\u003c\/p\u003e \u003cp\u003e7.4.3 Periodic motion and local stability 265\u003c\/p\u003e \u003cp\u003e7.5 Predictions and similations 268\u003c\/p\u003e \u003cp\u003e7.5.1 Bifurcation scenarios 268\u003c\/p\u003e \u003cp\u003e7.5.2 Analytical predictions 271\u003c\/p\u003e \u003cp\u003e7.5.3 Numberical illustractions 278\u003c\/p\u003e \u003cp\u003e7.6 Appendix 291\u003c\/p\u003e \u003cp\u003eReferences 295\u003c\/p\u003e \u003cp\u003eSubject index 297\u003c\/p\u003e\n\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":53186828730711,"sku":"9781118359457","price":999.99,"currency_code":"GBP","in_stock":false}],"url":"https:\/\/bookcurl.com\/products\/vibroimpact-dynamics-9781118359457","provider":"Book Curl","version":"1.0","type":"link"}