[PDF] On Small Period Large Amplitude Normal Modes Of Natural Hamiltonian Systems eBook

Author : E. W. C. van Groesen
Publisher :
Page : 25 pages
File Size : 48,58 MB
Release : 1984
Category : Mathematics
ISBN :

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Periodic solutions are investigated of the set of second order Hamiltonian equations -x = V'(x) for x(t) e R sub N, where the function V is even, has a certain monotonic behaviour on rays through the origin in R sub N and has superquadratic growth at infinity. It is proven that for T> 0 less than the smallest period of the linearized system (if non-trivial, else for all T), there exists a periodic solution of a special kind, a normal mode, which has minimal period T, has large amplitude (tending to infinity as T approaches limit of 0) and which minimizes the action functional on a naturally constrained set. If V has a direction of maximum increase this solution will be characterized completed. A condition for V is given, which is the same as in a multiplicity result for the prescribed energy case, that provides the existence of at least N distinct normal modes of minimal period T. (Author).

Author : P.H. Rabinowitz
Publisher : Springer Science & Business Media
Page : 288 pages
File Size : 50,20 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 9400939337

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This volume contains the proceedings of a NATO Advanced Research Workshop on Periodic Solutions of Hamiltonian Systems held in II Ciocco, Italy on October 13-17, 1986. It also contains some papers that were an outgrowth of the meeting. On behalf of the members of the Organizing Committee, who are also the editors of these proceedings, I thank all those whose contributions made this volume possible and the NATO Science Committee for their generous financial support. Special thanks are due to Mrs. Sally Ross who typed all of the papers in her usual outstanding fashion. Paul H. Rabinowitz Madison, Wisconsin April 2, 1987 xi 1 PERIODIC SOLUTIONS OF SINGULAR DYNAMICAL SYSTEMS Antonio Ambrosetti Vittorio Coti Zelati Scuola Normale Superiore SISSA Piazza dei Cavalieri Strada Costiera 11 56100 Pisa, Italy 34014 Trieste, Italy ABSTRACT. The paper contains a discussion on some recent advances in the existence of periodic solutions of some second order dynamical systems with singular potentials. The aim of this paper is to discuss some recent advances in th.e existence of periodic solutions of some second order dynamical systems with singular potentials.

Author : Jean Mawhin
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 47,30 MB
Release : 2013-04-17
Category : Science
ISBN : 1475720610

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FACHGEB The last decade has seen a tremendous development in critical point theory in infinite dimensional spaces and its application to nonlinear boundary value problems. In particular, striking results were obtained in the classical problem of periodic solutions of Hamiltonian systems. This book provides a systematic presentation of the most basic tools of critical point theory: minimization, convex functions and Fenchel transform, dual least action principle, Ekeland variational principle, minimax methods, Lusternik- Schirelmann theory for Z2 and S1 symmetries, Morse theory for possibly degenerate critical points and non-degenerate critical manifolds. Each technique is illustrated by applications to the discussion of the existence, multiplicity, and bifurcation of the periodic solutions of Hamiltonian systems. Among the treated questions are the periodic solutions with fixed period or fixed energy of autonomous systems, the existence of subharmonics in the non-autonomous case, the asymptotically linear Hamiltonian systems, free and forced superlinear problems. Application of those results to the equations of mechanical pendulum, to Josephson systems of solid state physics and to questions from celestial mechanics are given. The aim of the book is to introduce a reader familiar to more classical techniques of ordinary differential equations to the powerful approach of modern critical point theory. The style of the exposition has been adapted to this goal. The new topological tools are introduced in a progressive but detailed way and immediately applied to differential equation problems. The abstract tools can also be applied to partial differential equations and the reader will also find the basic references in this direction in the bibliography of more than 500 items which concludes the book. ERSCHEIN

Author :
Publisher :
Page : 376 pages
File Size : 22,98 MB
Release : 1995
Category : Aeronautics
ISBN :

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Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.

Author : Johannes F. Besseling
Publisher : Springer Science & Business Media
Page : 367 pages
File Size : 38,12 MB
Release : 2012-12-06
Category : Science
ISBN : 3642739334

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In many areas of mechanics the interplay between mathematics and physics is crucial for understanding not only underlying principles but also practical applications. This is particularly the case in hydrodynamics and elasticity. Over thirty articles in this volume discuss various aspects including perturbation methods and applications, instability, bifurcations and transition to chaos, multibody dynamics and control, mechanics and mathematics of non-classical materials, and new interactions of mathematics and mechanics. The book addresses scientists and engineers working in these areas including those interested in applied mathematical analysis.

Author : Tassos Bountis
Publisher : Springer Science & Business Media
Page : 277 pages
File Size : 26,15 MB
Release : 2012-04-03
Category : Science
ISBN : 364227305X

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This book introduces and explores modern developments in the well established field of Hamiltonian dynamical systems. It focuses on high degree-of-freedom systems and the transitional regimes between regular and chaotic motion. The role of nonlinear normal modes is highlighted and the importance of low-dimensional tori in the resolution of the famous FPU paradox is emphasized. Novel powerful numerical methods are used to study localization phenomena and distinguish order from strongly and weakly chaotic regimes. The emerging hierarchy of complex structures in such regimes gives rise to particularly long-lived patterns and phenomena called quasi-stationary states, which are explored in particular in the concrete setting of one-dimensional Hamiltonian lattices and physical applications in condensed matter systems. The self-contained and pedagogical approach is blended with a unique balance between mathematical rigor, physics insights and concrete applications. End of chapter exercises and (more demanding) research oriented problems provide many opportunities to deepen the reader’s insights into specific aspects of the subject matter. Addressing a broad audience of graduate students, theoretical physicists and applied mathematicians, this text combines the benefits of a reference work with those of a self-study guide for newcomers to the field.

Author : Matt Allen
Publisher : Springer
Page : 515 pages
File Size : 14,3 MB
Release : 2016-05-11
Category : Technology & Engineering
ISBN : 3319297635

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Dynamics of Coupled Structures, Volume 4. Proceedings of the 34th IMAC, A Conference and Exposition on Dynamics of Multiphysical Systems: From Active Materials to Vibroacoustics, 2016, the fourth volume of ten from the Conference brings together contributions to this important area of research and engineering. Th e collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on: • Experimental Dynamic Substructuring • Structural Coupling of Nonlinear Structures • Analytical/Numerical Modeling of Joints • Industrial Applications of Substructuring • Source Identifi cation & Transfer Path Analysis • Human Induced Vibrations • Damping & Friction