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Stability And Chaos In Celestial Mechanics
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Book Synopsis Stability and Chaos in Celestial Mechanics by : Alessandra Celletti
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.
Book Synopsis Celestial Encounters by : Florin Diacu
Download or read book Celestial Encounters written by Florin Diacu and published by Princeton University Press. This book was released on 2020-12-08 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: Celestial Encounters is for anyone who has ever wondered about the foundations of chaos. In 1888, the 34-year-old Henri Poincaré submitted a paper that was to change the course of science, but not before it underwent significant changes itself. "The Three-Body Problem and the Equations of Dynamics" won a prize sponsored by King Oscar II of Sweden and Norway and the journal Acta Mathematica, but after accepting the prize, Poincaré found a serious mistake in his work. While correcting it, he discovered the phenomenon of chaos. Starting with the story of Poincaré's work, Florin Diacu and Philip Holmes trace the history of attempts to solve the problems of celestial mechanics first posed in Isaac Newton's Principia in 1686. In describing how mathematical rigor was brought to bear on one of our oldest fascinations--the motions of the heavens--they introduce the people whose ideas led to the flourishing field now called nonlinear dynamics. In presenting the modern theory of dynamical systems, the models underlying much of modern science are described pictorially, using the geometrical language invented by Poincaré. More generally, the authors reflect on mathematical creativity and the roles that chance encounters, politics, and circumstance play in it.
Book Synopsis Predictability, Stability, and Chaos in N-Body Dynamical Systems by : Archie E. Roy
Download or read book Predictability, Stability, and Chaos in N-Body Dynamical Systems written by Archie E. Roy and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 581 pages. Available in PDF, EPUB and Kindle. Book excerpt: The reader will find in this volume the Proceedings of the NATO Advanced Study Institute held in Cortina d'Ampezzo, Italy between August 6 and August 17, 1990 under the title "Predictability, Stability, and Chaos in N-Body Dynamical Systems". The Institute was the latest in a series held at three-yearly inter vals from 1972 to 1987 in dynamical astronomy, theoretical mechanics and celestial mechanics. These previous institutes, held in high esteem by the international community of research workers, have resulted in a series of well-received Proceedings. The 1990 Institute attracted 74 participants from 16 countries, six outside the NATO group. Fifteen series of lectures were given by invited speakers; additionally some 40 valuable presentations were made by the younger participants, most of which are included in these Proceedings. The last twenty years in particular has been a time of increasingly rapid progress in tackling long-standing and also newly-arising problems in dynamics of N-body systems, point-mass and non-point-mass, a rate of progress achieved because of correspondingly rapid developments of new computer hardware and software together with the advent of new analytical techniques. It was a time of exciting progress culminating in the ability to carry out research programmes into the evolution of the outer Solar 8 System over periods of more than 10 years and to study star cluster and galactic models in unprecedented detail.
Book Synopsis Chaos and Stability in Planetary Systems by : Rudolf Dvorak
Download or read book Chaos and Stability in Planetary Systems written by Rudolf Dvorak and published by Springer. This book was released on 2009-09-02 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended as an introduction to the field of planetary systems at the postgraduate level. It consists of four extensive lectures on Hamiltonian dynamics, celestial mechanics, the structure of extrasolar planetary systems and the formation of planets. As such, this volume is particularly suitable for those who need to understand the substantial connections between these different topics.
Book Synopsis Chaos and Stability in Planetary Systems by : Rudolf Dvorak
Download or read book Chaos and Stability in Planetary Systems written by Rudolf Dvorak and published by Springer Science & Business Media. This book was released on 2006-01-13 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended as an introduction to the field of planetary systems at the postgraduate level. It consists of four extensive lectures on Hamiltonian dynamics, celestial mechanics, the structure of extrasolar planetary systems and the formation of planets. As such, this volume is particularly suitable for those who need to understand the substantial connections between these different topics.
Book Synopsis Capture Dynamics and Chaotic Motions in Celestial Mechanics by : Edward Belbruno
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.
Book Synopsis Celestial Dynamics by : Rudolf Dvorak
Download or read book Celestial Dynamics written by Rudolf Dvorak and published by John Wiley & Sons. This book was released on 2013-08-30 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by an internationally renowned expert author and researcher, this monograph fills the need for a book conveying the sophisticated tools needed to calculate exo-planet motion and interplanetary space flight. It is unique in considering the critical problems of dynamics and stability, making use of the software Mathematica, including supplements for practical use of the formulae. A must-have for astronomers and applied mathematicians alike.
Book Synopsis Chaos In Nature (Second Edition) by : Letellier Christophe
Download or read book Chaos In Nature (Second Edition) written by Letellier Christophe and published by World Scientific. This book was released on 2019-04-26 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the history of chaos theory, from celestial mechanics (three-body problem) to electronics and meteorology. Many illustrative examples of chaotic behaviors exist in various contexts found in nature (chemistry, astrophysics, biomedicine). This book includes the most popular systems from chaos theory (Lorenz, Rössler, van der Pol, Duffing, logistic map, Lozi map, Hénon map etc.) and introduces many other systems, some of them very rarely discussed in textbooks as well as in scientific papers. The contents are formulated with an original approach as compared to other books on chaos theory.
Book Synopsis Order and Chaos in Dynamical Astronomy by : George Contopoulos
Download or read book Order and Chaos in Dynamical Astronomy written by George Contopoulos and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is one of the first to provide a general overview of order and chaos in dynamical astronomy. The progress of the theory of chaos has a profound impact on galactic dynamics. It has even invaded celestial mechanics, since chaos was found in the solar system which in the past was considered as a prototype of order. The book provides a unifying approach to these topics from an author who has spent more than 50 years of research in the field. The first part treats order and chaos in general. The other two parts deal with order and chaos in galaxies and with other applications in dynamical astronomy, ranging from celestial mechanics to general relativity and cosmology.
Book Synopsis Instability, Chaos and Predictability in Celestial Mechanics and Stellar Dynamics by : International Astronomical Union. Colloquium
Download or read book Instability, Chaos and Predictability in Celestial Mechanics and Stellar Dynamics written by International Astronomical Union. Colloquium and published by . This book was released on 1993 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the International Astronomical Union Colloquium 132 held in Delhi, India, October 1990. Papers are divided into five sections: chaos, ergodic and stochastic motion, stellar systems and galaxies, triple and many body problem, and general celestial mechanics and stellar dynamics. Topics include algorithms for controlling chaos, vector
Book Synopsis Celestial Mechanics and Astrodynamics: Theory and Practice by : Pini Gurfil
Download or read book Celestial Mechanics and Astrodynamics: Theory and Practice written by Pini Gurfil and published by Springer. This book was released on 2016-07-28 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is designed as an introductory text and reference book for graduate students, researchers and practitioners in the fields of astronomy, astrodynamics, satellite systems, space sciences and astrophysics. The purpose of the book is to emphasize the similarities between celestial mechanics and astrodynamics, and to present recent advances in these two fields so that the reader can understand the inter-relations and mutual influences. The juxtaposition of celestial mechanics and astrodynamics is a unique approach that is expected to be a refreshing attempt to discuss both the mechanics of space flight and the dynamics of celestial objects. “Celestial Mechanics and Astrodynamics: Theory and Practice” also presents the main challenges and future prospects for the two fields in an elaborate, comprehensive and rigorous manner. The book presents homogenous and fluent discussions of the key problems, rendering a portrayal of recent advances in the field together with some basic concepts and essential infrastructure in orbital mechanics. The text contains introductory material followed by a gradual development of ideas interweaved to yield a coherent presentation of advanced topics.
Book Synopsis Celestial Mechanics by : Alessandra Celletti
Download or read book Celestial Mechanics written by Alessandra Celletti and published by Springer Science & Business Media. This book was released on 2007-06-24 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to demonstrate to a wider audience, as well as to a more skilled audience, the many fascinating aspects of modern celestial mechanics. It sets out to do this without the use of mathematics. After giving the reader the technical tools needed for a basic understanding of the underlying physical phenomena (using only elementary mathematics), facts and figures are provided on historical events, modern discoveries and future applications. Contents are divided into major topics where the three "souls" of modern celestial mechanics (dynamical systems, Solar System and stellar systems, spaceflight dynamics) play a major role.
Book Synopsis From Ordered To Chaotic Motion In Celestial Mechanics by : Yi-sui Sun
Download or read book From Ordered To Chaotic Motion In Celestial Mechanics written by Yi-sui Sun and published by World Scientific. This book was released on 2015-10-27 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a brief introduction to some basic but important problems in celestial mechanics, and particularly in the few-body problem, such as the permissible and forbidden region of motion, the evolution of moment of inertia of a system, and the orbital stability of asteroids in the solar system. All these are based on some main results in the authors' research works, which are related to the qualitative method of celestial mechanics and nonlinear dynamics. Some of these works are interdisciplinary, involving celestial mechanics, nonlinear dynamics and other disciplines. The book covers a variety of topics for dynamics in the solar system, including the comets, asteroids, planetary rings, Trojan asteroids, etc.As a senior scientist, Professor Sun shares his research experiences in this book. Readers may find plenty of information both about the theoretical and numerical analyses in celestial mechanics, and about the applications of theories and methods to dynamical problems in astronomy.
Book Synopsis From Newton to Chaos by : Archie E. Roy
Download or read book From Newton to Chaos written by Archie E. Roy and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 573 pages. Available in PDF, EPUB and Kindle. Book excerpt: The reader will find in this volume the Proceedings of the NATO Advanced Study Institute held in Cortina d' Ampezzo, Italy, between July 25 and August 6, 1993, under the title From Newton to Chaos: Modem Techniques for Understanding and Coping With Chaos inN-Body Dynamical Systems. This institute was the latest in a series of meetings held every three years from 1972 to 1990 in dynamical astronomy, theoretical mechanics and celestial mechanics. The proceedings from these institutes have been well-received in the international community of research workers in these disciplines. The present institute was well attended with 15 series of lectures being given by invited speakers: in addition some 40 presentations were made by the other participants. The majority of these contributions are included in these proceedings. The all-pervading influence of chaos in dynamical systems (of even a few variables) has now been universally recognised by researchers, a recognition forced on us by our ability, using powerful computer hardware and software, to tackle dynamical problems that until twenty-five years ago were intractable. Doubtless it was felt by many that these new techniques provided a break-through in celestial mechanics and its related disciplines. And so they were.
Book Synopsis Stable and Random Motions in Dynamical Systems by : Jurgen Moser
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 2001-05-06 with total page 214 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.
Book Synopsis Modern Celestial Mechanics by : Alessandro Morbidelli
Download or read book Modern Celestial Mechanics written by Alessandro Morbidelli and published by CRC Press. This book was released on 2002-05-16 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last 20 years, researchers in the field of celestial mechanics have achieved spectacular results in their effort to understand the structure and evolution of our solar system. Modern Celestial Mechanics uses a solid theoretical basis to describe recent results on solar system dynamics, and it emphasizes the dynamics of planets and of small bodies. To grasp celestial mechanics, one must comprehend the fundamental concepts of Hamiltonian systems theory, so this volume begins with an explanation of those concepts. Celestial mechanics itself is then considered, including the secular motion of planets and small bodies and mean motion resonances. Graduate students and researchers of astronomy and astrophysics will find Modern Celestial Mechanics an essential addition to their bookshelves.
Book Synopsis An Introduction to Celestial Mechanics by : Forest Ray Moulton
Download or read book An Introduction to Celestial Mechanics written by Forest Ray Moulton and published by . This book was released on 1914 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt:
