• Science

Order and Chaos in Dynamical Astronomy


Author: George Contopoulos
Publisher: Springer Science & Business Media
ISBN: 3662049171
Category: Science
Page: 624
View: 6153
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.

    • Science

Chaos and Stability in Planetary Systems


Author: Rudolf Dvorak,F. Freistetter,Jürgen Kurths
Publisher: Springer Science & Business Media
ISBN: 9783540282082
Category: Science
Page: 281
View: 1534
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.

    • Science

Stable and Random Motions in Dynamical Systems

With Special Emphasis on Celestial Mechanics (AM-77)
Author: Jurgen Moser
Publisher: Princeton University Press
ISBN: 1400882699
Category: Science
Page: 216
View: 6065
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.

    • Science

The Lidov-Kozai Effect - Applications in Exoplanet Research and Dynamical Astronomy


Author: Ivan Shevchenko
Publisher: Springer
ISBN: 3319435221
Category: Science
Page: 194
View: 2547
This book deals with an effect in celestial mechanics that has become quite important in exoplanet research. The Lidov-Kozai effect reveals itself in coherent periodic variations (which can be very large) of the inclination and eccentricity of an orbiting body in the presence of an inclined perturber. The effect is known to be important in the motion of many asteroids and planetary satellites. What is more, now it attracts more and more interest in the astronomical and astrophysical community due to its relevance for many exoplanetary systems. Recent years witnessed major advancements in its theory. It would be no exaggeration to say that nowadays the Lidov-Kozai effect becomes one of the most studied astrophysical effects. This book covers the multitude of the Lidov-Kozai effect’s modern applications and its theory developments. It will be useful for researchers and students working in astrophysics, celestial mechanics, stellar dynamics, theoretical mechanics, space missions design, depending on the interests of the reader. The book is self-contained. It provides the full detailed coverage of the effect’s theory and applications.

    • Science

Relativity and Gravitation

100 Years after Einstein in Prague
Author: Jiří Bičák,Tomáš Ledvinka
Publisher: Springer
ISBN: 3319067613
Category: Science
Page: 590
View: 6737
In early April 1911 Albert Einstein arrived in Prague to become full professor of theoretical physics at the German part of Charles University. It was there, for the first time, that he concentrated primarily on the problem of gravitation. Before he left Prague in July 1912 he had submitted the paper “Relativität und Gravitation: Erwiderung auf eine Bemerkung von M. Abraham” in which he remarkably anticipated what a future theory of gravity should look like. At the occasion of the Einstein-in-Prague centenary an international meeting was organized under a title inspired by Einstein's last paper from the Prague period: "Relativity and Gravitation, 100 Years after Einstein in Prague". The main topics of the conference included: classical relativity, numerical relativity, relativistic astrophysics and cosmology, quantum gravity, experimental aspects of gravitation and conceptual and historical issues. The conference attracted over 200 scientists from 31 countries, among them a number of leading experts in the field of general relativity and its applications. This volume includes abstracts of the plenary talks and full texts of contributed talks and articles based on the posters presented at the conference. These describe primarily original results of the authors. Full texts of the plenary talks are included in the volume "General Relativity, Cosmology and Astrophysics--Perspectives 100 Years after Einstein in Prague", eds. J. Bičák and T. Ledvinka, published also by Springer Verlag.

    • Mathematics

Chaos and Complexity in Astrophysics


Author: O. Regev
Publisher: Cambridge University Press
ISBN: 9780521855341
Category: Mathematics
Page: 455
View: 6208
A 2006 primer for researchers and graduate students; introduces and applies chaos techniques to specific astrophysical systems.

    • Science

Adventures in Order and Chaos

A Scientific Autobiography
Author: George Contopoulos
Publisher: Springer Science & Business Media
ISBN: 1402030401
Category: Science
Page: 200
View: 2019
For many years I was organizing a weekly seminar on dynamical astronomy, and I used to make some historical remarks on every subject, including some anecdotes from my contacts with many leading scientists over the years. I described also the development of various subjects and the emergence of new ideasindynamicalastronomy. Thenseveralpeoplepromptedmetowritedown these remarks, which cannot be found in papers, or books. Thus, I decided to write this book, which contains my experiences over the years. I hope that this book may be helpful to astronomy students all over the world. During my many years of teaching, as a visiting professor, in American Universities (1962-1994, Yale, Harvard, MIT, Cornell, Chicago, Maryland and Florida) I was impressed by the quality of my graduate students. Most of them were very bright, asking penetrating questions, and preparing their homework in a perfect way. In a few cases, instead of a ?nal examination, I assigned to them some small research projects and they presented their results at the end of the course. They were excellent in preparing the appropriate slides and in presenting their results in a concise and clear way.

    • Science

Stability and Chaos in Celestial Mechanics


Author: Alessandra Celletti
Publisher: Springer Science & Business Media
ISBN: 3540851461
Category: Science
Page: 264
View: 9193
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.

    • Science

Chaos in Astronomy

Conference 2007
Author: G. Contopoulos,P. A. Patsis
Publisher: Springer Science & Business Media
ISBN: 3540758267
Category: Science
Page: 497
View: 7829


    • Science

Solar System Dynamics


Author: Carl D. Murray,Stanley F. Dermott
Publisher: Cambridge University Press
ISBN: 9780521575973
Category: Science
Page: 592
View: 2850
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.

    • Mathematics

The Three-Body Problem and the Equations of Dynamics

Poincaré’s Foundational Work on Dynamical Systems Theory
Author: Henri Poincaré
Publisher: Springer
ISBN: 3319528998
Category: Mathematics
Page: 248
View: 4589
Here is an accurate and readable translation of a seminal article by Henri Poincaré that is a classic in the study of dynamical systems popularly called chaos theory. In an effort to understand the stability of orbits in the solar system, Poincaré applied a Hamiltonian formulation to the equations of planetary motion and studied these differential equations in the limited case of three bodies to arrive at properties of the equations’ solutions, such as orbital resonances and horseshoe orbits. Poincaré wrote for professional mathematicians and astronomers interested in celestial mechanics and differential equations. Contemporary historians of math or science and researchers in dynamical systems and planetary motion with an interest in the origin or history of their field will find his work fascinating.

    • Science

Tools of Radio Astronomy

Problems and Solutions ; with 8 Tables
Author: Thomas Wilson,Susanne Hüttemeister
Publisher: Springer Science & Business Media
ISBN: 9783540668022
Category: Science
Page: 162
View: 2817
This book contains graduate-level problems with carefully presented solutions and covers topics in radio astronomy. The problems are arranged following the content of the book “Tools of Radio Astronomy, 4th Ed.” by Rohlfs and T.L.Wilson (also available in the Astronomy and Astrophysics Library) on a chapter-by-chapter basis. Some of these problems have been formulated to provide an extension to the material presented in "Tools of Radio Astronomy".

    • Science

Theory of Orbits

Volume 1: Integrable Systems and Non-perturbative Methods
Author: Dino Boccaletti,Prof. Giuseppe Pucacco
Publisher: Springer Science & Business Media
ISBN: 3662033194
Category: Science
Page: 392
View: 3587
Half a century ago, S. Chandrasekhar wrote these words in the preface to his l celebrated and successful book: In this monograph an attempt has been made to present the theory of stellar dy namics as a branch of classical dynamics - a discipline in the same general category as celestial mechanics. [ ... J Indeed, several of the problems of modern stellar dy namical theory are so severely classical that it is difficult to believe that they are not already discussed, for example, in Jacobi's Vorlesungen. Since then, stellar dynamics has developed in several directions and at var ious levels, basically three viewpoints remaining from which to look at the problems encountered in the interpretation of the phenomenology. Roughly speaking, we can say that a stellar system (cluster, galaxy, etc.) can be con sidered from the point of view of celestial mechanics (the N-body problem with N » 1), fluid mechanics (the system is represented by a material con tinuum), or statistical mechanics (one defines a distribution function for the positions and the states of motion of the components of the system).

    • Earth sciences

Earth Sciences History

Journal of the History of the Earth Sciences Society
Author: N.A
Publisher: N.A
ISBN: N.A
Category: Earth sciences
Page: N.A
View: 8555

    • Science

Deep Simplicity

Chaos, Complexity and the Emergence of Life
Author: John Gribbin
Publisher: Penguin UK
ISBN: 0141042214
Category: Science
Page: 272
View: 1434
'Gribbin takes us through the basics with his customary talent for accessibility and clarity' Sunday Times The world around us can be a complex, confusing place. Earthquakes happen without warning, stock markets fluctuate, weather forecasters seldom seem to get it right - even other people continue to baffle us. How do we make sense of it all? In fact, John Gribbin reveals, our seemingly random universe is actually built on simple laws of cause and effect that can explain why, for example, just one vehicle braking can cause a traffic jam; why wild storms result from a slight atmospheric change; even how we evolved from the most basic materials. Like a zen painting, a fractal image or the pattern on a butterfly's wings, simple elements form the bedrock of a sophisticated whole. Synthesizing chaos and complexity theory for the perplexed, Deep Simplicity brilliantly illuminates the harmony underlying our existence.

    • Celestial mechanics.

Newton's Clock

Chaos in the Solar System
Author: Ivars Peterson
Publisher: Macmillan
ISBN: 0716723964
Category: Celestial mechanics.
Page: 317
View: 1928
Relates the history of the human search for an understanding of the motions of the moon and planets against the backdrop of the stars

    • Science

Galactic Dynamics

Second Edition
Author: James Binney,Scott Tremaine
Publisher: Princeton University Press
ISBN: 1400828724
Category: Science
Page: 904
View: 6284
Since it was first published in 1987, Galactic Dynamics has become the most widely used advanced textbook on the structure and dynamics of galaxies and one of the most cited references in astrophysics. Now, in this extensively revised and updated edition, James Binney and Scott Tremaine describe the dramatic recent advances in this subject, making Galactic Dynamics the most authoritative introduction to galactic astrophysics available to advanced undergraduate students, graduate students, and researchers. Every part of the book has been thoroughly overhauled, and many sections have been completely rewritten. Many new topics are covered, including N-body simulation methods, black holes in stellar systems, linear stability and response theory, and galaxy formation in the cosmological context. Binney and Tremaine, two of the world's leading astrophysicists, use the tools of theoretical physics to describe how galaxies and other stellar systems work, succinctly and lucidly explaining theoretical principles and their applications to observational phenomena. They provide readers with an understanding of stellar dynamics at the level needed to reach the frontiers of the subject. This new edition of the classic text is the definitive introduction to the field. ? A complete revision and update of one of the most cited references in astrophysics Provides a comprehensive description of the dynamical structure and evolution of galaxies and other stellar systems Serves as both a graduate textbook and a resource for researchers Includes 20 color illustrations, 205 figures, and more than 200 problems Covers the gravitational N-body problem, hierarchical galaxy formation, galaxy mergers, dark matter, spiral structure, numerical simulations, orbits and chaos, equilibrium and stability of stellar systems, evolution of binary stars and star clusters, and much more Companion volume to Galactic Astronomy, the definitive book on the phenomenology of galaxies and star clusters

Physics of Comets


Author: N.A
Publisher: N.A
ISBN: 9814466182
Category:
Page: N.A
View: 465

    • Science

Celestial Mechanics

The Waltz of the Planets
Author: Alessandra Celletti,Ettore Perozzi
Publisher: Springer Science & Business Media
ISBN: 0387685774
Category: Science
Page: 248
View: 5363
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.