Nonlinear Oscillations Of Hamiltonian Pdes PDF Download
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Author | : Massimiliano Berti |
Publisher | : Springer Science & Business Media |
Total Pages | : 191 |
Release | : 2007-10-01 |
Genre | : Mathematics |
ISBN | : 0817646809 |
Download Nonlinear Oscillations of Hamiltonian PDEs Book in PDF, ePub and Kindle
Many partial differential equations (PDEs) that arise in physics can be viewed as infinite-dimensional Hamiltonian systems. This monograph presents recent existence results of nonlinear oscillations of Hamiltonian PDEs, particularly of periodic solutions for completely resonant nonlinear wave equations. The text serves as an introduction to research in this fascinating and rapidly growing field. Graduate students and researchers interested in variational techniques and nonlinear analysis applied to Hamiltonian PDEs will find inspiration in the book.
Author | : Solomon Lefschetz |
Publisher | : Princeton University Press |
Total Pages | : 224 |
Release | : 2016-03-02 |
Genre | : Mathematics |
ISBN | : 1400881757 |
Download Contributions to the Theory of Nonlinear Oscillations (AM-41), Volume IV Book in PDF, ePub and Kindle
The description for this book, Contributions to the Theory of Nonlinear Oscillations (AM-41), Volume IV, will be forthcoming.
Author | : Frank H. Clarke |
Publisher | : |
Total Pages | : 26 |
Release | : 1979 |
Genre | : Boundary value problems |
ISBN | : |
Download Nonlinear Oscillations and Boundary-Value Problems for Hamiltonian Systems Book in PDF, ePub and Kindle
Hamilton's differential equations are basic in the study of theoretical mechanics. A particular class of motions of interest for such systems of equations are the periodic ones, which correspond to oscillations (vibrations) of the underlying physical system; the absence of such motions is usually associated with resonance phenomena. In this paper we give conditions on the Hamiltonian function H which guarantee the existence of periodic orbits, as well as other more general types of motions. One distinction with previous work on the subject is that we consider forced vibrations arising from external driving forces; another is that the solutions in question are characterized directly as the solutions of a specific minimization problem (i.e., we obtain a 'variational principle'), a feature which could prove useful for computational purposes.
Author | : Solomon Lefschetz |
Publisher | : Princeton University Press |
Total Pages | : 128 |
Release | : 2016-03-02 |
Genre | : Mathematics |
ISBN | : 1400882702 |
Download Contributions to the Theory of Nonlinear Oscillations (AM-29), Volume II Book in PDF, ePub and Kindle
These two new collections, numbers 28 and 29 respectively in the Annals of Mathematics Studies, continue the high standard set by the earlier Annals Studies 20 and 24 by bringing together important contributions to the theories of games and of nonlinear differential equations.
Author | : Walter Craig |
Publisher | : Springer Science & Business Media |
Total Pages | : 450 |
Release | : 2008-02-17 |
Genre | : Mathematics |
ISBN | : 1402069642 |
Download Hamiltonian Dynamical Systems and Applications Book in PDF, ePub and Kindle
This volume is the collected and extended notes from the lectures on Hamiltonian dynamical systems and their applications that were given at the NATO Advanced Study Institute in Montreal in 2007. Many aspects of the modern theory of the subject were covered at this event, including low dimensional problems. Applications are also presented to several important areas of research, including problems in classical mechanics, continuum mechanics, and partial differential equations.
Author | : P.S Landa |
Publisher | : Springer Science & Business Media |
Total Pages | : 550 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 9401587639 |
Download Nonlinear Oscillations and Waves in Dynamical Systems Book in PDF, ePub and Kindle
A rich variety of books devoted to dynamical chaos, solitons, self-organization has appeared in recent years. These problems were all considered independently of one another. Therefore many of readers of these books do not suspect that the problems discussed are divisions of a great generalizing science - the theory of oscillations and waves. This science is not some branch of physics or mechanics, it is a science in its own right. It is in some sense a meta-science. In this respect the theory of oscillations and waves is closest to mathematics. In this book we call the reader's attention to the present-day theory of non-linear oscillations and waves. Oscillatory and wave processes in the systems of diversified physical natures, both periodic and chaotic, are considered from a unified poin t of view . The relation between the theory of oscillations and waves, non-linear dynamics and synergetics is discussed. One of the purposes of this book is to convince reader of the necessity of a thorough study popular branches of of the theory of oscillat ions and waves, and to show that such science as non-linear dynamics, synergetics, soliton theory, and so on, are, in fact , constituent parts of this theory. The primary audiences for this book are researchers having to do with oscillatory and wave processes, and both students and post-graduate students interested in a deep study of the general laws and applications of the theory of oscillations and waves.
Author | : Hannes Uecker |
Publisher | : SIAM |
Total Pages | : 380 |
Release | : 2021-08-19 |
Genre | : Mathematics |
ISBN | : 1611976618 |
Download Numerical Continuation and Bifurcation in Nonlinear PDEs Book in PDF, ePub and Kindle
This book provides a hands-on approach to numerical continuation and bifurcation for nonlinear PDEs in 1D, 2D, and 3D. Partial differential equations (PDEs) are the main tool to describe spatially and temporally extended systems in nature. PDEs usually come with parameters, and the study of the parameter dependence of their solutions is an important task. Letting one parameter vary typically yields a branch of solutions, and at special parameter values, new branches may bifurcate. After a concise review of some analytical background and numerical methods, the author explains the free MATLAB package pde2path by using a large variety of examples with demo codes that can be easily adapted to the reader's given problem. Numerical Continuation and Bifurcation in Nonlinear PDEs will appeal to applied mathematicians and scientists from physics, chemistry, biology, and economics interested in the numerical solution of nonlinear PDEs, particularly the parameter dependence of solutions. It can be used as a supplemental text in courses on nonlinear PDEs and modeling and bifurcation.
Author | : Lamberto Cesari |
Publisher | : Princeton University Press |
Total Pages | : 304 |
Release | : 2016-03-02 |
Genre | : Mathematics |
ISBN | : 1400882648 |
Download Contributions to the Theory of Nonlinear Oscillations (AM-45), Volume V Book in PDF, ePub and Kindle
The description for this book, Contributions to the Theory of Nonlinear Oscillations (AM-45), Volume V, will be forthcoming.
Author | : Ahmed Aly Kamel |
Publisher | : |
Total Pages | : 60 |
Release | : 1970 |
Genre | : Nonlinear oscillations |
ISBN | : |
Download Perturbation Method in the Theory of Nonlinear Oscillations Book in PDF, ePub and Kindle
Author | : Maurizio Garrione |
Publisher | : Springer Nature |
Total Pages | : 115 |
Release | : 2019-10-31 |
Genre | : Mathematics |
ISBN | : 3030302180 |
Download Nonlinear Equations for Beams and Degenerate Plates with Piers Book in PDF, ePub and Kindle
This book develops a full theory for hinged beams and degenerate plates with multiple intermediate piers with the final purpose of understanding the stability of suspension bridges. New models are proposed and new tools are provided for the stability analysis. The book opens by deriving the PDE’s based on the physical models and by introducing the basic framework for the linear stationary problem. The linear analysis, in particular the behavior of the eigenvalues as the position of the piers varies, enables the authors to tackle the stability issue for some nonlinear evolution beam equations, with the aim of determining the “best position” of the piers within the beam in order to maximize its stability. The study continues with the analysis of a class of degenerate plate models. The torsional instability of the structure is investigated, and again, the optimal position of the piers in terms of stability is discussed. The stability analysis is carried out by means of both analytical tools and numerical experiments. Several open problems and possible future developments are presented. The qualitative analysis provided in the book should be seen as the starting point for a precise quantitative study of more complete models, taking into account the action of aerodynamic forces. This book is intended for a two-fold audience. It is addressed both to mathematicians working in the field of Differential Equations, Nonlinear Analysis and Mathematical Physics, due to the rich number of challenging mathematical questions which are discussed and left as open problems, and to Engineers interested in mechanical structures, since it provides the theoretical basis to deal with models for the dynamics of suspension bridges with intermediate piers. More generally, it may be enjoyable for readers who are interested in the application of Mathematics to real life problems.