Chaos and Stability in Planetary Systems PDF Download

Author: Rudolf Dvorak
Publisher: Springer Science & Business Media
ISBN: 9783540282082
Category : Science
Languages : en
Pages : 304

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Book Description
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.

Author: Alessandra Celletti
Publisher: Springer Science & Business Media
ISBN: 3540851461
Category : Science
Languages : en
Pages : 265

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Book Description
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: Rudolf Dvorak
Publisher: Springer
ISBN: 9783540814078
Category : Science
Languages : en
Pages : 281

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Book Description
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.

Author: Sylvio Ferraz-Mello
Publisher: Springer Nature
ISBN: 3031458168
Category : Science
Languages : en
Pages : 176

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Book Description
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.

Author: Carl D. Murray
Publisher: Cambridge University Press
ISBN: 1139936158
Category : Science
Languages : en
Pages : 612

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Book Description
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.

Author: Ivars Peterson
Publisher: Macmillan
ISBN: 0716723964
Category : Science
Languages : en
Pages : 341

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Book Description
With his critically acclaimed best-sellers The Mathematical Tourism and Islands of Truth, Ivars Peterson took readers to the frontiers of modern mathematics. His new book provides an up-to-date look at one of science's greatest detective stories: the search for order in the workings of the solar system. In the late 1600s, Sir Isaac Newton provided what astronomers had long sought: a seemingly reliable way of calculating planetary orbits and positions. Newton's laws of motion and his coherent, mathematical view of the universe dominated scientific discourse for centuries. At the same time, observers recorded subtle, unexpected movements of the planets and other bodies, suggesting that the solar system is not as placid and predictable as its venerable clock work image suggests. Today, scientists can go beyond the hand calculations, mathematical tables, and massive observational logs that limited the explorations of Newton, Copernicus, Galileo, Kepler, Tycho Brahe, and others. Using supercomputers to simulate the dynamics of the solar system, modern astronomers are learning more about the motions they observe and uncovering some astonishing examples of chaotic behavior in the heavens. Nonetheless, the long-term stability of the solar system remains a perplexing, unsolved issue, with each step toward its resolution exposing additional uncertainties and deeper mysteries. To show how our view of the solar system has changed from clocklike precision to chaos and complexity, Newton's Clock describes the development of celestial mechanics through the ages - from the star charts of ancient navigators to the seminal discoveries of the 17th century from the crucial work of Poincare to thestartling, sometimes controversial findings and theories made possible by modern mathematics and computer simulations. The result makes for entertaining and provocative reading, equal parts science, history and intellectual adventure.

Author: David D. Nolte
Publisher: Oxford University Press
ISBN: 0192528505
Category : Science
Languages : en
Pages : 384

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Book Description
Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.

Author: A. Milani
Publisher: Springer Science & Business Media
ISBN: 9401111480
Category : Science
Languages : en
Pages : 531

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Book Description
THE MEETING The IAU Symposium 160 ASTEROIDS COMETS METEORS 1999 has been held at Villa Carlotta in Belgirate, on the shore of Lago Maggiore (Italy), from June 14 to June 18, 1993. It has been organized by the Astronomical Observatory of Torino and by the Lunar and Planetary Institute of Houston. It has been a very large meeting, with 323 registered participants from 38 countries. The scientific program included 29 invited reviews, 106 oral communications, and 215 posters. The subjects covered included all the aspects of the studies of the minor bodies of the solar system, including asteroids, comets, meteors, meteorites, interplanetary dust, with special focus on the interrelationships between these. The meeting was structured as follows. 5 morning plenary sessions have been devoted to invited reviews on: (1) search programs (2) populations of small bodies (3) dynamics (4) physical observations and modelling (5) origin and evolution. Two afternoon plenary sessions have been devoted to space missions to small bodies and to interrelationships between the different populations. The afternoon parallel sessions have been devoted to: dynamics of comets; Toutatis, Ida, Gaspra; physical processes in cometary comae and tails; meteorites; the cosmogonic message from cometary nuclei; physics of asteroids; the interplanetary dust complex; comet nuclei; meteors; composition and material properties of comets; dynamics of asteroids.

Author: Steven H. Strogatz
Publisher: CRC Press
ISBN: 0429961111
Category : Mathematics
Languages : en
Pages : 532

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Book Description
This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

Author: Sylvio Ferraz-Mello
Publisher: Springer Science & Business Media
ISBN: 9780792317821
Category : Science
Languages : en
Pages : 432

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Book Description
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.