Stable And Random Motions In Dyamical Systems With Special Emphasis On Celestial Mechanics
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Author | : Jurgen Moser |
Publisher | : Princeton University Press |
Total Pages | : 216 |
Release | : 2016-03-02 |
Genre | : Science |
ISBN | : 1400882699 |
Download Stable and Random Motions in Dynamical Systems Book in PDF, Epub and Kindle
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.
Author | : Jürgen Moser |
Publisher | : |
Total Pages | : 198 |
Release | : 1973 |
Genre | : Celestial mechanics |
ISBN | : |
Download Stable and Random Motions in Dynamical Systems: with Special Emphasis on Celestial Mechanics Book in PDF, Epub and Kindle
The Description for this book, Stable and Random Motions in Dynamical Systems: With Special Emphasis on Celestial Mechanics. (AM-77), will be forthcoming.
Author | : G. B. Folland |
Publisher | : |
Total Pages | : 198 |
Release | : 1973 |
Genre | : Algebraic number theory |
ISBN | : 9780691081120 |
Download Stable and Random Motions in Dynamical Systems: with Special Emphasis on Celestial Mechanics Book in PDF, Epub and Kindle
Author | : Jürgen Moser |
Publisher | : |
Total Pages | : 198 |
Release | : 1973 |
Genre | : |
ISBN | : |
Download Stable and Random Motions in Dynamical Systems. With Secial Emphasis on Celestial Mechanics. Hermann Weyl Lectures, The Institute for Advanced Study Book in PDF, Epub and Kindle
Author | : Jurgen Moser |
Publisher | : |
Total Pages | : 198 |
Release | : 1973 |
Genre | : |
ISBN | : |
Download Stable and Random Motions in Dyamical Systems with Special Emphasis on Celestial Mechanics Book in PDF, Epub and Kindle
Author | : Edward Belbruno |
Publisher | : Princeton University Press |
Total Pages | : 232 |
Release | : 2018-06-05 |
Genre | : Mathematics |
ISBN | : 069118643X |
Download Capture Dynamics and Chaotic Motions in Celestial Mechanics Book in PDF, Epub and Kindle
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.
Author | : Alessandra Celletti |
Publisher | : Springer Science & Business Media |
Total Pages | : 265 |
Release | : 2010-03-10 |
Genre | : Science |
ISBN | : 3540851461 |
Download Stability and Chaos in Celestial Mechanics Book in PDF, Epub and Kindle
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.
Author | : Jürgen Moser |
Publisher | : American Mathematical Soc. |
Total Pages | : 266 |
Release | : 2005 |
Genre | : Mathematics |
ISBN | : 0821835777 |
Download Notes on Dynamical Systems Book in PDF, Epub and Kindle
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.
Author | : Florin Diacu |
Publisher | : Princeton University Press |
Total Pages | : 258 |
Release | : 1999-03-28 |
Genre | : Mathematics |
ISBN | : 9780691005454 |
Download Celestial Encounters Book in PDF, Epub and Kindle
Celestial Encounters traces the history of attempts to solve the problem of celestial mechanics first posited in Isaac Newton's Principia in 1686. More generally, the authors reflect on mathematical creativity and the roles that chance encounters, politics, and circumstance play in it. 23 halftones. 64 line illustrations.
Author | : Harry Dankowicz |
Publisher | : World Scientific |
Total Pages | : 224 |
Release | : 1997-12-16 |
Genre | : Science |
ISBN | : 981449710X |
Download Chaotic Dynamics In Hamiltonian Systems: With Applications To Celestial Mechanics Book in PDF, Epub and Kindle
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.