Screen LibraryBifurcation and chaos in nonsmooth mechanical systems /
This book presents the theoretical frame for studying lumped nonsmooth dynamical systems: the mathematical methods are recalled, and adapted numerical methods are introduced (differential inclusions, maximal monotone operators, Filippov theory, Aizerman theory, etc.). Tools available for the analysi...
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| Main Authors: | |
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| Corporate Authors: | |
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| Published: |
World Scientific Pub. Co.,
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| Publisher Address: | Singapore ; River Edge, N.J. : |
| Publication Dates: | 2003. |
| Literature type: | eBook |
| Language: | English |
| Series: |
World Scientific series on nonlinear science. Series A ;
v. 45 |
| Subjects: | |
| Online Access: |
http://www.worldscientific.com/worldscibooks/10.1142/5342#t=toc |
| Summary: |
This book presents the theoretical frame for studying lumped nonsmooth dynamical systems: the mathematical methods are recalled, and adapted numerical methods are introduced (differential inclusions, maximal monotone operators, Filippov theory, Aizerman theory, etc.). Tools available for the analysis of classical smooth nonlinear dynamics (stability analysis, the Melnikov method, bifurcation scenarios, numerical integrators, solvers, etc.) are extended to the nonsmooth frame. Many models and applications arising from mechanical engineering, electrical circuits, material behavior and civil en |
| Carrier Form: | 1 online resource (xvii,543pages) : illustrations (some color). |
| Bibliography: | Includes bibliographical references (pages 507-530) and index. |
| ISBN: | 9789812564801 (electronic bk.) |
| CLC: | TH11-05 |
| Contents: |
1. Introduction to discontinuous ODEs. 1.1. Introduction. 1.2. Filippov's theory. 1.3. Aizerman's theory. 1.4. Examples. 1.5. Boundary value problem -- 2. Mathematical background for multivalued formulations. 2.1. Origin of nonlinearities. 2.2. Smooth and nonsmooth nonlinearities. 2.3. Examples and dynamical equilibria. 2.4. Existence and uniqueness. 2.5. Stochastic frame -- 3. Numerical schemes and analytical methods. 3.1. Numerical schemes. 3.2. Analytical methods -- 4. Properties of numerical schemes. 4.1. Dynamics of systems with friction or elastoplastic terms. 4.2. Systems with impacts 11. Modelling the dynamical behaviour of elasto-plastic systems. 11.1. Rheological systems with "friction" -- 12. A mechanical system with 7 DOF. 12.1. Mathematical model. 12.2. Numerical results and comments for finite k3 -- 13. Stability of singular periodic motions in single degree of freedom vibro-impact oscillators and grazing bifurcations. 13.1. Introduction. 13.2. Mechanical system and change of coordinates. 13.3. Local expansion of the Poincar map. 13.4. Stability of the nondifferentiable fixed point. 13.5. Applications. 13.6. Conclusion -- 14. Triple pendulum with impacts. 14.1. Int |