Download or read book Stable and Random Motions in Dynamical Systems written by Jurgen Moser and published by Princeton University Press. This book was released on 2016-03-02 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Stable and Random Motions in Dynamical Systems with Special Emphasis on Celestial Mechanics written by Jürgen Moser and published by . This book was released on 1973 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Description for this book, Stable and Random Motions in Dynamical Systems: With Special Emphasis on Celestial Mechanics. (AM-77), will be forthcoming.

Download or read book Stable and Random Motions in Dynamical Systems with Special Emphasis on Celestial Mechanics written by G. B. Folland and published by . This book was released on 1973 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Capture Dynamics and Chaotic Motions in Celestial Mechanics written by Edward Belbruno and published by Princeton University Press. This book was released on 2018-06-05 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes a revolutionary new approach to determining low energy routes for spacecraft and comets by exploiting regions in space where motion is very sensitive (or chaotic). It also represents an ideal introductory text to celestial mechanics, dynamical systems, and dynamical astronomy. Bringing together wide-ranging research by others with his own original work, much of it new or previously unpublished, Edward Belbruno argues that regions supporting chaotic motions, termed weak stability boundaries, can be estimated. Although controversial until quite recently, this method was in fact first applied in 1991, when Belbruno used a new route developed from this theory to get a stray Japanese satellite back on course to the moon. This application provided a major verification of his theory, representing the first application of chaos to space travel. Since that time, the theory has been used in other space missions, and NASA is implementing new applications under Belbruno's direction. The use of invariant manifolds to find low energy orbits is another method here addressed. Recent work on estimating weak stability boundaries and related regions has also given mathematical insight into chaotic motion in the three-body problem. Belbruno further considers different capture and escape mechanisms, and resonance transitions. Providing a rigorous theoretical framework that incorporates both recent developments such as Aubrey-Mather theory and established fundamentals like Kolmogorov-Arnold-Moser theory, this book represents an indispensable resource for graduate students and researchers in the disciplines concerned as well as practitioners in fields such as aerospace engineering.

Download or read book Notes on Dynamical Systems written by Jurgen Moser and published by American Mathematical Soc.. This book was released on 2005 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the field of dynamical systems, in particular, to the special class of Hamiltonian systems. The authors aimed at keeping the requirements of mathematical techniques minimal but giving detailed proofs and many examples and illustrations from physics and celestial mechanics. After all, the celestial $N$-body problem is the origin of dynamical systems and gave rise in the past to many mathematical developments. Jurgen Moser (1928-1999) was a professor atthe Courant Institute, New York, and then at ETH Zurich. He served as president of the International Mathematical Union and received many honors and prizes, among them the Wolf Prize in mathematics. Jurgen Moser is the author of several books, among them Stable and Random Motions in DynamicalSystems. Eduard Zehnder is a professor at ETH Zurich. He is coauthor with Helmut Hofer of the book Symplectic Invariants and Hamiltonian Dynamics. Information for our distributors: Titles in this series are copublished with the Courant Institute of Mathematical Sciences at New York University.

Download or read book Stability and Chaos in Celestial Mechanics written by Alessandra Celletti and published by Springer Science & Business Media. This book was released on 2010-03-10 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Chaotic Dynamics in Hamiltonian Systems written by Harry Dankowicz and published by World Scientific. This book was released on 1997-12-16 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the past hundred years investigators have learned the significance of complex behavior in deterministic systems. The potential applications of this discovery are as numerous as they are encouraging. This text clearly presents the mathematical foundations of chaotic dynamics, including methods and results at the forefront of current research. The book begins with a thorough introduction to dynamical systems and their applications. It goes on to develop the theory of regular and stochastic behavior in higher-degree-of-freedom Hamiltonian systems, covering topics such as homoclinic chaos, KAM theory, the Melnikov method, and Arnold diffusion. Theoretical discussions are illustrated by a study of the dynamics of small circumasteroidal grains perturbed by solar radiation pressure. With alternative derivations and proofs of established results substituted for those in the standard literature, this work serves as an important source for researchers, students and teachers. Skillfully combining in-depth mathematics and actual physical applications, this book will be of interest to the applied mathematician, the theoretical mechanical engineer and the dynamical astronomer alike. Contents:IntroductionHamiltonian SystemsHomoclinic OrbitsThe Perturbation ApproachApplication — Radiation Pressure IGeometry and Dynamics in Many Degrees-of-FreedomApplication — Radiation Pressure IIOutlookIndex Readership: Students and researchers in dynamical systems, classical mechanics and dynamical astronomy. keywords:Chaos;Dynamical Systems;Hamiltonian Systems;Hamiltonian Mechanics;Celestial Mechanics;Radiation Pressure;Arnold Diffusion;Melnikov's Method

Download or read book KAM Stability and Celestial Mechanics written by Alessandra Celletti and published by American Mathematical Soc.. This book was released on 2007 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Orbital Motion written by A.E. Roy and published by CRC Press. This book was released on 2020-07-14 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: Long established as one of the premier references in the fields of astronomy, planetary science, and physics, the fourth edition of Orbital Motion continues to offer comprehensive coverage of the analytical methods of classical celestial mechanics while introducing the recent numerical experiments on the orbital evolution of gravitating masses and the astrodynamics of artificial satellites and interplanetary probes. Following detailed reviews of earlier editions by distinguished lecturers in the USA and Europe, the author has carefully revised and updated this edition. Each chapter provides a thorough introduction to prepare you for more complex concepts, reflecting a consistent perspective and cohesive organization that is used throughout the book. A noted expert in the field, the author not only discusses fundamental concepts, but also offers analyses of more complex topics, such as modern galactic studies and dynamical parallaxes. New to the Fourth Edition: * Numerous updates and reorganization of all chapters to encompass new methods * New results from recent work in areas such as satellite dynamics * New chapter on the Caledonian symmetrical n-body problem Extending its coverage to meet a growing need for this subject in satellite and aerospace engineering, Orbital Motion, Fourth Edition remains a top reference for postgraduate and advanced undergraduate students, professionals such as engineers, and serious amateur astronomers.

Download or read book Mathematical Aspects of Classical and Celestial Mechanics written by Vladimir I. Arnold and published by Springer Science & Business Media. This book was released on 2007-07-05 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book A Century in Books written by Princeton University Press Staff and published by Princeton University Press. This book was released on 2021-10-12 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: It all began atop a drugstore in Princeton, New Jersey, in November 1905. From its modest beginnings, Princeton University Press was to become one of the world's most important scholarly publishers, embracing a wealth of disciplines that have enriched our cultural, academic, and scientific landscape. Both as a tribute to our authors and to celebrate our centenary, Princeton University Press here presents A Century in Books. This beautifully designed volume highlights 100 of the nearly 8,000 books we have published. Necessarily winnowed from a much larger list, these books best typify what has been most lasting, most defining, and most distinctive about our publishing history--from Einstein's The Meaning of Relativity (1922) to the numerous mathematical and other works that marked the Press's watershed decade of the 1940s, including von Neumann and Morgenstern's Theory of Games and Economic Behavior; from milestones of literary criticism by Erich Auerbach and Northop Frye to George Kennan's Pulitzer Prize-winning book on Soviet-American relations; from Milton Friedman and Anna Jacobson Schwartz's A Monetary History of the United States, 1867-1960 to more recent landmarks such as L. Luca Cavalli-Sforza, Paolo Menozzi, and Alberto Piazza's The History and Geography of Human Genes and Robert Shiller's Irrational Exuberance. In addition to succinct descriptions of the 100 titles and a short introduction on the history of the Press, the book features five essays by prominent scholars and writers: Michael Wood discusses the impact on Princeton University Press of intellectuals who fled Nazi Germany and authored many influential books. Anthony Grafton recounts our rich publishing tradition in history, politics, and culture. Sylvia Nasar traces our evolution into a leading voice in economics publishing. Daniel Kevles reflects on Einstein, a figure of special importance to Princeton. And Lord Robert May writes on our long-standing tradition of publishing in mathematics and science. A Century in Books is more than a celebration of 100 years of publishing at Princeton University Press--it is a treasure trove of 100 years of books that have added to the richness of twentieth-century intellectual life.

Download or read book Quasi Periodic Motions in Families of Dynamical Systems written by Hendrik W. Broer and published by Springer. This book was released on 2009-01-25 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the phenomenon of quasi-periodic motion in dynamical systems. Such a motion in the phase space densely fills up an invariant torus. This phenomenon is most familiar from Hamiltonian dynamics. Hamiltonian systems are well known for their use in modelling the dynamics related to frictionless mechanics, including the planetary and lunar motions. In this context the general picture appears to be as follows. On the one hand, Hamiltonian systems occur that are in complete order: these are the integrable systems where all motion is confined to invariant tori. On the other hand, systems exist that are entirely chaotic on each energy level. In between we know systems that, being sufficiently small perturbations of integrable ones, exhibit coexistence of order (invariant tori carrying quasi-periodic dynamics) and chaos (the so called stochastic layers). The Kolmogorov-Arnol'd-Moser (KAM) theory on quasi-periodic motions tells us that the occurrence of such motions is open within the class of all Hamiltonian systems: in other words, it is a phenomenon persistent under small Hamiltonian perturbations. Moreover, generally, for any such system the union of quasi-periodic tori in the phase space is a nowhere dense set of positive Lebesgue measure, a so called Cantor family. This fact implies that open classes of Hamiltonian systems exist that are not ergodic. The main aim of the book is to study the changes in this picture when other classes of systems - or contexts - are considered.

Download or read book Adventures in Celestial Mechanics written by Victor G. Szebehely and published by John Wiley & Sons. This book was released on 2008-07-11 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Hamiltonian Dynamical Systems written by R.S MacKay and published by CRC Press. This book was released on 2020-08-18 with total page 808 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical mechanics is a subject that is teeming with life. However, most of the interesting results are scattered around in the specialist literature, which means that potential readers may be somewhat discouraged by the effort required to obtain them. Addressing this situation, Hamiltonian Dynamical Systems includes some of the most significant papers in Hamiltonian dynamics published during the last 60 years. The book covers bifurcation of periodic orbits, the break-up of invariant tori, chaotic behavior in hyperbolic systems, and the intricacies of real systems that contain coexisting order and chaos. It begins with an introductory survey of the subjects to help readers appreciate the underlying themes that unite an apparently diverse collection of articles. The book concludes with a selection of papers on applications, including in celestial mechanics, plasma physics, chemistry, accelerator physics, fluid mechanics, and solid state mechanics, and contains an extensive bibliography. The book provides a worthy introduction to the subject for anyone with an undergraduate background in physics or mathematics, and an indispensable reference work for researchers and graduate students interested in any aspect of classical mechanics.

Download or read book Handbook of Dynamical Systems written by H. Broer and published by Elsevier. This book was released on 2010-11-10 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, the authors present a collection of surveys on various aspects of the theory of bifurcations of differentiable dynamical systems and related topics. By selecting these subjects, they focus on those developments from which research will be active in the coming years. The surveys are intended to educate the reader on the recent literature on the following subjects: transversality and generic properties like the various forms of the so-called Kupka-Smale theorem, the Closing Lemma and generic local bifurcations of functions (so-called catastrophe theory) and generic local bifurcations in 1-parameter families of dynamical systems, and notions of structural stability and moduli. Covers recent literature on various topics related to the theory of bifurcations of differentiable dynamical systems Highlights developments that are the foundation for future research in this field Provides material in the form of surveys, which are important tools for introducing the bifurcations of differentiable dynamical systems

Download or read book Models and Methods in the Philosophy of Science Selected Essays written by Patrick Suppes and published by Springer Science & Business Media. This book was released on 1993-05-31 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book publishes 31 of the author's selected papers which have appeared, with one exception, since 1970. The papers cover a wide range of topics in the philosophy of science. Part I is concerned with general methodology, including formal and axiomatic methods in science. Part II is concerned with causality and explanation. The papers extend the author's earlier work on a probabilistic theory of causality. The papers in Part III are concerned with probability and measurement, especially foundational questions about probability. Part IV consists of several papers, including two historical ones, on the foundations of physics, with the main emphasis being on quantum mechanics. Part V, the longest part, is on the foundations of psychology and includes papers mainly on learning and perception. The book is aimed at philosophers of science, scientists concerned with the methodology of the social sciences, and mathematical psychologists interested in theories of learning, perception and measurement.

Download or read book Progress and Challenges in Dynamical Systems written by Santiago Ibáñez and published by Springer Science & Business Media. This book was released on 2013-09-20 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains papers based on talks given at the International Conference Dynamical Systems: 100 years after Poincaré held at the University of Oviedo, Gijón in Spain, September 2012. It provides an overview of the state of the art in the study of dynamical systems. This book covers a broad range of topics, focusing on discrete and continuous dynamical systems, bifurcation theory, celestial mechanics, delay difference and differential equations, Hamiltonian systems and also the classic challenges in planar vector fields. It also details recent advances and new trends in the field, including applications to a wide range of disciplines such as biology, chemistry, physics and economics. The memory of Henri Poincaré, who laid the foundations of the subject, inspired this exploration of dynamical systems. In honor of this remarkable mathematician, theoretical physicist, engineer and philosopher, the authors have made a special effort to place the reader at the frontiers of current knowledge in the discipline.