E-Book, Englisch, Band 163, 482 Seiten
Bernardo / Budd / Champneys Piecewise-smooth Dynamical Systems
1. Auflage 2008
ISBN: 978-1-84628-708-4
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
Theory and Applications
E-Book, Englisch, Band 163, 482 Seiten
Reihe: Applied Mathematical Sciences
ISBN: 978-1-84628-708-4
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
This book presents a coherent framework for understanding the dynamics of piecewise-smooth and hybrid systems. An informal introduction expounds the ubiquity of such models via numerous. The results are presented in an informal style, and illustrated with many examples. The book is aimed at a wide audience of applied mathematicians, engineers and scientists at the beginning postgraduate level. Almost no mathematical background is assumed other than basic calculus and algebra.
Autoren/Hrsg.
Weitere Infos & Material
1;Preface;6
1.1;Acknowledgments;11
2;Contents;14
3;Glossary;20
4;1 Introduction;23
4.1;1.1 Why piecewise smooth?;23
4.2;1.2 Impact oscillators;25
4.3;1.3 Other examples of piecewise-smooth systems;50
4.4;1.4 Non-smooth one-dimensional maps;61
5;2 Qualitative theory of non-smooth dynamical systems;69
5.1;2.1 Smooth dynamical systems;69
5.2;2.2 Piecewise-smooth dynamical systems;93
5.3;2.3 Other formalisms for non-smooth systems;105
5.4;2.4 Stability and bifurcation of non-smooth systems;115
5.5;2.5 Discontinuity mappings;125
5.6;2.6 Numerical methods;136
6;3 Border-collision in piecewise-linear continuous maps;143
6.1;3.1 Locally piecewise-linear continuous maps;143
6.2;3.2 Bifurcation of the simplest orbits;150
6.3;3.3 Equivalence of border-collision classi.cation methods;159
6.4;3.4 One-dimensional piecewise-linear maps;165
6.5;3.5 Two-dimensional piecewise-linear normal form maps;176
6.6;3.6 Maps that are noninvertible on one side;181
6.7;3.7 Effects of nonlinear perturbations;191
7;4 Bifurcations in general piecewise-smooth maps;193
7.1;4.1 Types of piecewise-smooth maps;193
7.2;4.2 Piecewise-smooth discontinuous maps;196
7.3;4.3 Square-root maps;210
7.4;4.4 Higher-order piecewise-smooth maps;232
8;5 Boundary equilibrium bifurcations in flows;241
8.1;5.1 Piecewise-smooth continuous flows;241
8.2;5.2 Filippov flows;255
8.3;5.3 Equilibria of impacting hybrid systems;267
9;6 Limit cycle bifurcations in impacting systems;275
9.1;6.1 The impacting class of hybrid systems;275
9.2;6.2 Discontinuity mappings near grazing;287
9.3;6.3 Grazing bifurcations of periodic orbits;301
9.4;6.4 Chattering and the geometry of the grazing manifold;317
9.5;6.5 Multiple collision bifurcation;324
10;7 Limit cycle bifurcations in piecewise-smooth flows;329
10.1;7.1 De.nitions and examples;329
10.2;7.2 Grazing with a smooth boundary;340
10.3;7.3 Boundary-intersection crossing bifurcations;362
11;8 Sliding bifurcations in Filippov systems;377
11.1;8.1 Four possible cases;377
11.2;8.2 Motivating example: a relay feedback system;386
11.3;8.3 Derivation of the discontinuity mappings;395
11.4;8.4 Mapping for a whole period: normal form maps;405
11.5;8.5 Unfolding the grazing-sliding bifurcation;418
11.6;8.6 Other cases;425
12;9 Further applications and extensions;431
12.1;9.1 Experimental impact oscillators: noise and parameter sensitivity;431
12.2;9.2 Rattling gear teeth: the similarity of impacting and piecewise- smooth systems;444
12.3;9.3 A hydraulic damper: non-smooth invariant tori;456
12.4;9.4 Two-parameter sliding bifurcations in friction oscillators;470
13;References;481
14;Index;497
