Stable And Random Motions In Dynamical Systems With Special Emphasis On Celestial Mechanics
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Stable And Random Motions In Dynamical Systems With Special Emphasis On Celestial Mechanics
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Author : Jürgen Moser
language : en
Publisher:
Release Date : 1973
Stable And Random Motions In Dynamical Systems With Special Emphasis On Celestial Mechanics written by Jürgen Moser and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Celestial mechanics categories.
The Description for this book, Stable and Random Motions in Dynamical Systems: With Special Emphasis on Celestial Mechanics. (AM-77), will be forthcoming.
Stable And Random Motions In Dynamical Systems
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Author : Jurgen Moser
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02
Stable And Random Motions In Dynamical Systems written by Jurgen Moser and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Science categories.
For centuries, astronomers have been interested in the motions of the planets and in methods to calculate their orbits. Since Newton, mathematicians have been fascinated by the related N-body problem. They seek to find solutions to the equations of motion for N masspoints interacting with an inverse-square-law force and to determine whether there are quasi-periodic orbits or not. Attempts to answer such questions have led to the techniques of nonlinear dynamics and chaos theory. In this book, a classic work of modern applied mathematics, Jürgen Moser presents a succinct account of two pillars of the theory: stable and chaotic behavior. He discusses cases in which N-body motions are stable, covering topics such as Hamiltonian systems, the (Moser) twist theorem, and aspects of Kolmogorov-Arnold-Moser theory. He then explores chaotic orbits, exemplified in a restricted three-body problem, and describes the existence and importance of homoclinic points. This book is indispensable for mathematicians, physicists, and astronomers interested in the dynamics of few- and many-body systems and in fundamental ideas and methods for their analysis. After thirty years, Moser's lectures are still one of the best entrées to the fascinating worlds of order and chaos in dynamics.
Stable And Random Motions In Dynamical Systems With Special Emphasis On Celestial Mechanics
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Author : G. B. Folland
language : en
Publisher:
Release Date : 1973
Stable And Random Motions In Dynamical Systems With Special Emphasis On Celestial Mechanics written by G. B. Folland and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Algebraic number theory categories.
Stability And Chaos In Celestial Mechanics
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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.
Kam Stability And Celestial Mechanics
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Author : Alessandra Celletti
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Kam Stability And Celestial Mechanics written by Alessandra Celletti 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 2007 with Mathematics categories.
KAM theory is a powerful tool apt to prove perpetual stability in Hamiltonian systems, which are a perturbation of integrable ones. The smallness requirements for its applicability are well known to be extremely stringent. A long standing problem, in this context, is the application of KAM theory to ``physical systems'' for ``observable'' values of the perturbation parameters. The authors consider the Restricted, Circular, Planar, Three-Body Problem (RCP3BP), i.e., the problem of studying the planar motions of a small body subject to the gravitational attraction of two primary bodies revolving on circular Keplerian orbits (which are assumed not to be influenced by the small body). When the mass ratio of the two primary bodies is small, the RCP3BP is described by a nearly-integrable Hamiltonian system with two degrees of freedom; in a region of phase space corresponding to nearly elliptical motions with non-small eccentricities, the system is well described by Delaunay variables. The Sun-Jupiter observed motion is nearly circular and an asteroid of the Asteroidal belt may be assumed not to influence the Sun-Jupiter motion. The Jupiter-Sun mass ratio is slightly less than 1/1000. The authors consider the motion of the asteroid 12 Victoria taking into account only the Sun-Jupiter gravitational attraction regarding such a system as a prototype of a RCP3BP. for values of mass ratios up to 1/1000, they prove the existence of two-dimensional KAM tori on a fixed three-dimensional energy level corresponding to the observed energy of the Sun-Jupiter-Victoria system. Such tori trap the evolution of phase points ``close'' to the observed physical data of the Sun-Jupiter-Victoria system. As a consequence, in the RCP3BP description, the motion of Victoria is proven to be forever close to an elliptical motion. The proof is based on: 1) a new iso-energetic KAM theory; 2) an algorithm for computing iso-energetic, approximate Lindstedt series; 3) a computer-aided application of 1)+2) to the Sun-Jupiter-Victoria system. The paper is self-contained but does not include the ($\sim$ 12000 lines) computer programs, which may be obtained by sending an e-mail to one of the authors.
Hamiltonian Dynamics And Celestial Mechanics
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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.
Adventures In Celestial Mechanics
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Author : Victor G. Szebehely
language : en
Publisher: John Wiley & Sons
Release Date : 2008-07-11
Adventures In Celestial Mechanics written by Victor G. Szebehely and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-11 with Technology & Engineering categories.
A fascinating introduction to the basic principles of orbital mechanics It has been three hundred years since Isaac Newton first formulated laws to explain the orbits of the Moon and the planets of our solar system. In so doing he laid the groundwork for modern science's understanding of the workings of the cosmos and helped pave the way to the age of space exploration. Adventures in Celestial Mechanics offers students an enjoyable way to become acquainted with the basic principles involved in the motions of natural and human-made bodies in space. Packed with examples in which these principles are applied to everything from a falling stone to the Sun, from space probes to galaxies, this updated and revised Second Edition is an ideal introduction to celestial mechanics for students of astronomy, physics, and aerospace engineering. Other features that helped make the first edition of this book the text of choice in colleges and universities across North America include: * Lively historical accounts of important discoveries in celestial mechanics and the men and women who made them * Superb illustrations, photographs, charts, and tables * Helpful chapter-end examples and problem sets
Mathematical Aspects Of Classical And Celestial Mechanics
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Author : Vladimir I. Arnold
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-07-05
Mathematical Aspects Of Classical And Celestial Mechanics written by Vladimir I. Arnold 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 2007-07-05 with Mathematics categories.
The main purpose of the book is to acquaint mathematicians, physicists and engineers with classical mechanics as a whole, in both its traditional and its contemporary aspects. As such, it describes the fundamental principles, problems, and methods of classical mechanics, with the emphasis firmly laid on the working apparatus, rather than the physical foundations or applications. Chapters cover the n-body problem, symmetry groups of mechanical systems and the corresponding conservation laws, the problem of the integrability of the equations of motion, the theory of oscillations and perturbation theory.
Stability Theory And Related Topics In Dynamical Systems
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Author : K Shiraiwa
language : en
Publisher: World Scientific
Release Date : 1989-09-01
Stability Theory And Related Topics In Dynamical Systems written by K Shiraiwa and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-09-01 with Mathematics categories.
Lectures On Dynamical Systems
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Author : Eduard Zehnder
language : en
Publisher: European Mathematical Society
Release Date : 2010
Lectures On Dynamical Systems written by Eduard Zehnder and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Dynamics categories.
This book originated from an introductory lecture course on dynamical systems given by the author for advanced students in mathematics and physics at ETH Zurich. The first part centers around unstable and chaotic phenomena caused by the occurrence of homoclinic points. The existence of homoclinic points complicates the orbit structure considerably and gives rise to invariant hyperbolic sets nearby. The orbit structure in such sets is analyzed by means of the shadowing lemma, whose proof is based on the contraction principle. This lemma is also used to prove S. Smale's theorem about the embedding of Bernoulli systems near homoclinic orbits. The chaotic behavior is illustrated in the simple mechanical model of a periodically perturbed mathematical pendulum. The second part of the book is devoted to Hamiltonian systems. The Hamiltonian formalism is developed in the elegant language of the exterior calculus. The theorem of V. Arnold and R. Jost shows that the solutions of Hamiltonian systems which possess sufficiently many integrals of motion can be written down explicitly and for all times. The existence proofs of global periodic orbits of Hamiltonian systems on symplectic manifolds are based on a variational principle for the old action functional of classical mechanics. The necessary tools from variational calculus are developed. There is an intimate relation between the periodic orbits of Hamiltonian systems and a class of symplectic invariants called symplectic capacities. From these symplectic invariants one derives surprising symplectic rigidity phenomena. This allows a first glimpse of the fast developing new field of symplectic topology.