Hamiltonian Dynamics And Celestial Mechanics
DOWNLOAD
Download Hamiltonian Dynamics And Celestial Mechanics PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Hamiltonian Dynamics And Celestial Mechanics book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Hamiltonian Dynamics And Celestial Mechanics
DOWNLOAD
Author : Donald Saari
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Hamiltonian Dynamics And Celestial Mechanics written by Donald Saari and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
The symbiotic of these two topics creates a natural combination for a conference on dynamics. Topics covered include twist maps, the Aubrey-Mather theory, Arnold diffusion, qualitative and topological studies of systems, and variational methods, as well as specific topics such as Melnikov's procedure and the singularity properties of particular systems.
Introduction To Hamiltonian Dynamical Systems And The N Body Problem
DOWNLOAD
Author : Kenneth Meyer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Introduction To Hamiltonian Dynamical Systems And The N Body Problem written by Kenneth Meyer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
The theory of Hamiltonian systems is a vast subject which can be studied from many different viewpoints. This book develops the basic theory of Hamiltonian differential equations from a dynamical systems point of view. That is, the solutions of the differential equations are thought of as curves in a phase space and it is the geometry of these curves that is the important object of study. The analytic underpinnings of the subject are developed in detail. The last chapter on twist maps has a more geometric flavor. It was written by Glen R. Hall. The main example developed in the text is the classical N-body problem, i.e., the Hamiltonian system of differential equations which describe the motion of N point masses moving under the influence of their mutual gravitational attraction. Many of the general concepts are applied to this example. But this is not a book about the N-body problem for its own sake. The N-body problem is a subject in its own right which would require a sizable volume of its own. Very few of the special results which only apply to the N-body problem are given.
Stability And Chaos In Celestial Mechanics
DOWNLOAD
Author : Alessandra Celletti
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-03-10
Stability And Chaos In Celestial Mechanics written by Alessandra Celletti and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-03-10 with Science categories.
This overview of classical celestial mechanics focuses the interplay with dynamical systems. Paradigmatic models introduce key concepts – order, chaos, invariant curves and cantori – followed by the investigation of dynamical systems with numerical methods.
Hamiltonian Systems And Celestial Mechanics
DOWNLOAD
Author : Ernesto A Lacomba
language : en
Publisher: World Scientific
Release Date : 1993-04-30
Hamiltonian Systems And Celestial Mechanics written by Ernesto A Lacomba and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-04-30 with categories.
This book deals with the fundamentals of wave optics, polarization, interference, diffraction, imaging, and the origin, properties, and optical effects of turbulence in the Earth's atmosphere. Techniques developed during the last few decades to overcome atmospheric image degradation (including passive methods, speckle interferometry in particular, and active methods such as adaptive optics), are highlighted. Also discussed are high resolution sensors, image processing, and the astronomical results obtained with these techniques.
Convexity Methods In Hamiltonian Mechanics
DOWNLOAD
Author : Ivar Ekeland
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Convexity Methods In Hamiltonian Mechanics written by Ivar Ekeland and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
In the case of completely integrable systems, periodic solutions are found by inspection. For nonintegrable systems, such as the three-body problem in celestial mechanics, they are found by perturbation theory: there is a small parameter € in the problem, the mass of the perturbing body for instance, and for € = 0 the system becomes completely integrable. One then tries to show that its periodic solutions will subsist for € -# 0 small enough. Poincare also introduced global methods, relying on the topological properties of the flow, and the fact that it preserves the 2-form L~=l dPi 1\ dqi' The most celebrated result he obtained in this direction is his last geometric theorem, which states that an area-preserving map of the annulus which rotates the inner circle and the outer circle in opposite directions must have two fixed points. And now another ancient theme appear: the least action principle. It states that the periodic solutions of a Hamiltonian system are extremals of a suitable integral over closed curves. In other words, the problem is variational. This fact was known to Fermat, and Maupertuis put it in the Hamiltonian formalism. In spite of its great aesthetic appeal, the least action principle has had little impact in Hamiltonian mechanics. There is, of course, one exception, Emmy Noether's theorem, which relates integrals ofthe motion to symmetries of the equations. But until recently, no periodic solution had ever been found by variational methods.
Construction Of Mappings For Hamiltonian Systems And Their Applications
DOWNLOAD
Author : Sadrilla S. Abdullaev
language : en
Publisher: Springer
Release Date : 2006-08-02
Construction Of Mappings For Hamiltonian Systems And Their Applications written by Sadrilla S. Abdullaev and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-02 with Science categories.
Based on the method of canonical transformation of variables and the classical perturbation theory, this innovative book treats the systematic theory of symplectic mappings for Hamiltonian systems and its application to the study of the dynamics and chaos of various physical problems described by Hamiltonian systems. It develops a new, mathematically-rigorous method to construct symplectic mappings which replaces the dynamics of continuous Hamiltonian systems by the discrete ones. Applications of the mapping methods encompass the chaos theory in non-twist and non-smooth dynamical systems, the structure and chaotic transport in the stochastic layer, the magnetic field lines in magnetically confinement devices of plasmas, ray dynamics in waveguides, etc. The book is intended for postgraduate students and researches, physicists and astronomers working in the areas of plasma physics, hydrodynamics, celestial mechanics, dynamical astronomy, and accelerator physics. It should also be useful for applied mathematicians involved in analytical and numerical studies of dynamical systems.
Classical And Quantum Dynamics Of Constrained Hamiltonian Systems
DOWNLOAD
Author : Heinz J. Rothe
language : en
Publisher: World Scientific
Release Date : 2010
Classical And Quantum Dynamics Of Constrained Hamiltonian Systems written by Heinz J. Rothe and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
This book is an introduction to the field of constrained Hamiltonian systems and their quantization, a topic which is of central interest to theoretical physicists who wish to obtain a deeper understanding of the quantization of gauge theories, such as describing the fundamental interactions in nature. Beginning with the early work of Dirac, the book covers the main developments in the field up to more recent topics, such as the field-antifield formalism of Batalin and Vilkovisky, including a short discussion of how gauge anomalies may be incorporated into this formalism. The book is comprehensive and well-illustrated with examples, enables graduate students to follow the literature on this subject without much problems, and to perform research in this field.
Introduction To The Perturbation Theory Of Hamiltonian Systems
DOWNLOAD
Author : Dmitry Treschev
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-10-08
Introduction To The Perturbation Theory Of Hamiltonian Systems written by Dmitry Treschev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-08 with Mathematics categories.
This book is an extended version of lectures given by the ?rst author in 1995–1996 at the Department of Mechanics and Mathematics of Moscow State University. We believe that a major part of the book can be regarded as an additional material to the standard course of Hamiltonian mechanics. In comparison with the original Russian 1 version we have included new material, simpli?ed some proofs and corrected m- prints. Hamiltonian equations ?rst appeared in connection with problems of geometric optics and celestial mechanics. Later it became clear that these equations describe a large classof systemsin classical mechanics,physics,chemistry,and otherdomains. Hamiltonian systems and their discrete analogs play a basic role in such problems as rigid body dynamics, geodesics on Riemann surfaces, quasi-classic approximation in quantum mechanics, cosmological models, dynamics of particles in an accel- ator, billiards and other systems with elastic re?ections, many in?nite-dimensional models in mathematical physics, etc. In this book we study Hamiltonian systems assuming that they depend on some parameter (usually?), where for?= 0 the dynamics is in a sense simple (as a rule, integrable). Frequently such a parameter appears naturally. For example, in celestial mechanics it is accepted to take? equal to the ratio: the mass of Jupiter over the mass of the Sun. In other cases it is possible to introduce the small parameter ar- ?cially.
Notes On Hamiltonian Dynamical Systems
DOWNLOAD
Author : Antonio Giorgilli
language : en
Publisher: Cambridge University Press
Release Date : 2022-05-05
Notes On Hamiltonian Dynamical Systems written by Antonio Giorgilli and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-05 with Science categories.
Starting with the basics of Hamiltonian dynamics and canonical transformations, this text follows the historical development of the theory culminating in recent results: the Kolmogorov–Arnold–Moser theorem, Nekhoroshev's theorem and superexponential stability. Its analytic approach allows students to learn about perturbation methods leading to advanced results. Key topics covered include Liouville's theorem, the proof of Poincaré's non-integrability theorem and the nonlinear dynamics in the neighbourhood of equilibria. The theorem of Kolmogorov on persistence of invariant tori and the theory of exponential stability of Nekhoroshev are proved via constructive algorithms based on the Lie series method. A final chapter is devoted to the discovery of chaos by Poincaré and its relations with integrability, also including recent results on superexponential stability. Written in an accessible, self-contained way with few prerequisites, this book can serve as an introductory text for senior undergraduate and graduate students.