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Dynamical Chaos in Planetary Systems

Dynamical Chaos in Planetary Systems
Author: Ivan I. Shevchenko
Publisher: Springer Nature
Total Pages: 376
Release: 2020-08-31
Genre: Science
ISBN: 3030521443
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This is the first monograph dedicated entirely to problems of stability and chaotic behaviour in planetary systems and its subsystems. The author explores the three rapidly developing interplaying fields of resonant and chaotic dynamics of Hamiltonian systems, the dynamics of Solar system bodies, and the dynamics of exoplanetary systems. The necessary concepts, methods and tools used to study dynamical chaos (such as symplectic maps, Lyapunov exponents and timescales, chaotic diffusion rates, stability diagrams and charts) are described and then used to show in detail how the observed dynamical architectures arise in the Solar system (and its subsystems) and in exoplanetary systems. The book concentrates, in particular, on chaotic diffusion and clearing effects. The potential readership of this book includes scientists and students working in astrophysics, planetary science, celestial mechanics, and nonlinear dynamics.

Solar System Dynamics

Solar System Dynamics
Author: Carl D. Murray
Publisher: Cambridge University Press
Total Pages: 612
Release: 2000-02-13
Genre: Science
ISBN: 1139936158
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The Solar System is a complex and fascinating dynamical system. This is the first textbook to describe comprehensively the dynamical features of the Solar System and to provide students with all the mathematical tools and physical models they need to understand how it works. It is a benchmark publication in the field of planetary dynamics and destined to become a classic. Clearly written and well illustrated, Solar System Dynamics shows how a basic knowledge of the two- and three-body problems and perturbation theory can be combined to understand features as diverse as the tidal heating of Jupiter's moon Io, the origin of the Kirkwood gaps in the asteroid belt, and the radial structure of Saturn's rings. Problems at the end of each chapter and a free Internet Mathematica® software package are provided. Solar System Dynamics provides an authoritative textbook for courses on planetary dynamics and celestial mechanics. It also equips students with the mathematical tools to tackle broader courses on dynamics, dynamical systems, applications of chaos theory and non-linear dynamics.

Chaotic Dynamics in Planetary Systems

Chaotic Dynamics in Planetary Systems
Author: Sylvio Ferraz-Mello
Publisher: Springer Nature
Total Pages: 176
Release: 2023-12-31
Genre: Science
ISBN: 3031458168
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The main theme of the book is the presentation of techniques used to identify chaotic behavior in the evolution of conservative mechanical systems and their application to astronomical systems. It results from graduate courses given by the author over the years both at university and at several international summer schools. Along the book surfaces of section, Lyapunov characteristic exponents, frequency maps, MEGNO, dense grid maps, etc., are presented and discussed in connection with the applications. The initial chapter is devoted to the presentation of the main ideas of the chaotic dynamics of conservative systems in plain language so that they can be accessible to a wide range of professionals and students of physical sciences. The applications are mainly related to the motions in the solar system and extrasolar planetary systems. Another chapter is devoted to the applications to asteroids showing how the asteroidal belt is sculpted by chaos and resonances. The contrasting existence of gaps in the distribution of the asteroids and groups of asteroids in resonances is thoroughly discussed. The interest in applications to planetary systems is growing since the discovery of systems of resonant planets around some stars of the solar neighborhood. Exoplanets added a lot of cases to a problem that was before restricted to the planets of our solar system. The book includes an account of results already existing about compact systems.

Chaos, Resonance and Collective Dynamical Phenomena in the Solar System

Chaos, Resonance and Collective Dynamical Phenomena in the Solar System
Author: Sylvio Ferraz-Mello
Publisher: Springer Science & Business Media
Total Pages: 432
Release: 1992-05-31
Genre: Science
ISBN: 9780792317821
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This symposium was devoted to a new celestial mechanics whose aim has become the study of such `objects' as the planetary system, planetary rings, the asteroidal belt, meteor swarms, satellite systems, comet families, the zodiacal cloud, the preplanetary nebula, etc. When the three-body problem is considered instead of individual orbits we are, now, looking for the topology of extended regions of its phase space. This Symposium was one step in the effort to close the ties between two scientific families: the observationally-oriented scientists and the theoretically-oriented scientists.

Chaos and Stability in Planetary Systems

Chaos and Stability in Planetary Systems
Author: Rudolf Dvorak
Publisher: Springer Science & Business Media
Total Pages: 304
Release: 2006-01-13
Genre: Science
ISBN: 9783540282082
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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.

Chaos and Stability in Planetary Systems

Chaos and Stability in Planetary Systems
Author: Rudolf Dvorak
Publisher: Springer
Total Pages: 281
Release: 2009-09-02
Genre: Science
ISBN: 9783540814078
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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.

Chaotic Worlds: from Order to Disorder in Gravitational N-Body Dynamical Systems

Chaotic Worlds: from Order to Disorder in Gravitational N-Body Dynamical Systems
Author: B.A. Steves
Publisher: Springer Science & Business Media
Total Pages: 342
Release: 2006-09-22
Genre: Science
ISBN: 1402047061
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Based on the recent NATO Advanced Study Institute "Chaotic Worlds: From Order to Disorder in Gravitational N-Body Dynamical Systems", this state of the art textbook, written by internationally renowned experts, provides an invaluable reference volume for all students and researchers in gravitational n-body systems. The contributions are especially designed to give a systematic development from the fundamental mathematics which underpin modern studies of ordered and chaotic behaviour in n-body dynamics to their application to real motion in planetary systems. This volume presents an up-to-date synoptic view of the subject.

Dynamical Chaos

Dynamical Chaos
Author: Michael V. Berry
Publisher: Princeton University Press
Total Pages: 209
Release: 2014-07-14
Genre: Science
ISBN: 1400860199
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The leading scientists who gave these papers under the sponsorship of the Royal Society in early 1987 provide reviews of facets of the subject of chaos ranging from the practical aspects of mirror machines for fusion power to the pure mathematics of geodesics on surfaces of negative curvature. The papers deal with systems in which chaotic conditions arise from initial value problems with unique solutions, as opposed to those where chaos is produced by the introduction of noise from an external source. Table of Contents Diagnosis of Dynamical Systems with Fluctuating Parameters D. Ruelle Nonlinear Dynamics, Chaos, and Complex Cardiac Arrhythmias L. Glass, A. L. Goldberger, M. Courtemanche, and A. Shrier Chaos and the Dynamics of Biological Populations R. M. May Fractal Bifurcation Sets, Renormalization Strange Sets, and Their Universal Invariants D. A. Rand From Chaos to Turbulence in Bnard Convection A. Libchaber Dynamics of Convection N. O. Weiss Chaos: A Mixed Metaphor for Turbulence E. A. Spiegel Arithmetical Theory of Anosov Diffeomorphisms F. Vivaldi Chaotic Behavior in the Solar System J. Wisdom Chaos in Hamiltonian Systems I. C. Percival Semi-Classical Quantization, Adiabatic Invariants, and Classical Chaos W. P. Reinhardt and I. Dana Particle Confinement and Adiabatic Invariance B. V. Chirikov Some Geometrical Models of Chaotic Dynamics C. Series The Bakerian Lecture: Quantum Chaology M. V. Berry Originally published in 1989. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Dynamics of Planetary Systems

Dynamics of Planetary Systems
Author: Scott Tremaine
Publisher: Princeton University Press
Total Pages: 641
Release: 2023-02-07
Genre: Science
ISBN: 0691244227
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An introduction to celestial mechanics for advanced undergraduates, graduate students, and researchers new to the field Celestial mechanics—the study of the movement of planets, satellites, and smaller bodies such as comets—is one of the oldest subjects in the physical sciences. Since the mid-twentieth century, the field has experienced a renaissance due to advances in space flight, digital computing, numerical mathematics, nonlinear dynamics, and chaos theory, and the discovery of exoplanets. This modern, authoritative introduction to planetary system dynamics reflects these recent developments and discoveries and is suitable for advanced undergraduate and graduate students as well as researchers. The book treats both traditional subjects, such as the two-body and three-body problems, lunar theory, and Hamiltonian perturbation theory, as well as a diverse range of other topics, including chaos in the solar system, comet dynamics, extrasolar planets, planetesimal dynamics, resonances, tidal friction and disruption, and more. The book provides readers with all the core concepts, tools, and methods needed to conduct research in the subject. Provides an authoritative introduction that reflects recent advances in the field Topics treated include Andoyer variables, co-orbital satellites and quasi-satellites, Hill’s problem, the Milankovich equations, Colombo’s top and Cassini states, the Yarkovsky and YORP effects, orbit determination for extrasolar planets, and more More than 100 end-of-book problems elaborate on concepts not fully covered in the main text Appendixes summarize the necessary background material Suitable for advanced undergraduates and graduate students; some knowledge of Hamiltonian mechanics and methods of mathematical physics (vectors, matrices, special functions, etc.) required Solutions manual available on request for instructors who adopt the book for a course

New Developments in the Dynamics of Planetary Systems

New Developments in the Dynamics of Planetary Systems
Author: Rudolf Dvorak
Publisher: Springer Science & Business Media
Total Pages: 375
Release: 2013-06-29
Genre: Science
ISBN: 9401724148
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It is now a well-established tradition that every four years, at the end of winter, a group of 'celestial mechanicians' from all over the world gather in the Austrian Alps at the invitation of R. Dvorak. This time the colloquium was held at Badhofgastein from March 19 to March 25, 2000 and was devoted to the 'New Developments in the Dynamics of Planetary Systems'. The papers covered a large range of questions of current interest: t- oretical questions (resonances, KAM theory, transport, ... ) and questions about numerical tools (synthetic elements, indicators of chaos, ... ) were particularly well represented; of course planetary theories and Near Earth Objects were also quite popular. Three special lectures were delivered in honor of deceased colleagues whom, to our dismay, we will no longer meet at the 'Austrian Colloquia'. W. Jefferys delivered the Heinrich Eichhorn lecture on 'Statistics for the Twenty-first Century Astrometry', a topic on which Heinrich Eichhorn was a specialist. A. Roy delivered a lecture honoring Victor Szehebely on 'Lifting the Darkness: Science in the Third Millenium', in which in wove anecdotes and remembrances of Victor which moved the audience very much. A. Lemaitre spoke in honor of Michele Moons on 'Mech anism of Capture in External Resonance'. The end of her talk was devoted to a short and moving biography of Michele illustrated by many slides.