Gravitational Few Body Dynamics

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Gravitational Few-Body Dynamics

Author : Seppo Mikkola
Publisher : Cambridge University Press
ISBN 13 : 1108871399
Total Pages : 257 pages
Book Rating : 4.1/5 (88 download)

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Book Synopsis Gravitational Few-Body Dynamics by : Seppo Mikkola

Download or read book Gravitational Few-Body Dynamics written by Seppo Mikkola and published by Cambridge University Press. This book was released on 2020-04-16 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using numerical integration, it is possible to predict the individual motions of a group of a few celestial objects interacting with each other gravitationally. In this introduction to the few-body problem, a key figure in developing more efficient methods over the past few decades summarizes and explains them, covering both basic analytical formulations and numerical methods. The mathematics required for celestial mechanics and stellar dynamics is explained, starting with two-body motion and progressing through classical methods for planetary system dynamics. This first part of the book can be used as a short course on celestial mechanics. The second part develops the contemporary methods for which the author is renowned - symplectic integration and various methods of regularization. This volume explains the methodology of the subject for graduate students and researchers in celestial mechanics and astronomical dynamics with an interest in few-body dynamics and the regularization of the equations of motion.

Gravitational Few-Body Dynamics

Author : Seppo Mikkola
Publisher : Cambridge University Press
ISBN 13 : 1108491294
Total Pages : 257 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis Gravitational Few-Body Dynamics by : Seppo Mikkola

Download or read book Gravitational Few-Body Dynamics written by Seppo Mikkola and published by Cambridge University Press. This book was released on 2020-04-16 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to the few-body problem progresses from two-body motion and classical planetary dynamics to modern numerical methods.

The Restless Universe Applications of Gravitational N-Body Dynamics to Planetary Stellar and Galactic Systems

Author : Bonnie Steves
Publisher : CRC Press
ISBN 13 : 1420033301
Total Pages : 403 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis The Restless Universe Applications of Gravitational N-Body Dynamics to Planetary Stellar and Galactic Systems by : Bonnie Steves

Download or read book The Restless Universe Applications of Gravitational N-Body Dynamics to Planetary Stellar and Galactic Systems written by Bonnie Steves and published by CRC Press. This book was released on 2019-05-07 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Restless Universe: Applications of Gravitational N-Body Dynamics to Planetary Stellar and Galactic Systems stimulates the cross-fertilization of ideas, methods, and applications among the different communities who work in the gravitational N-body problem arena, across diverse fields of astrophysics. The chapters and topics cover three broad the

The Restless Universe Applications of Gravitational N-body Dynamics to Planetary Stellar and Galactic Systems

Author :
Publisher :
ISBN 13 : 9781138406230
Total Pages : pages
Book Rating : 4.4/5 (62 download)

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Book Synopsis The Restless Universe Applications of Gravitational N-body Dynamics to Planetary Stellar and Galactic Systems by :

Download or read book The Restless Universe Applications of Gravitational N-body Dynamics to Planetary Stellar and Galactic Systems written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Gravitational Million-Body Problem

Author : D. C. Heggie
Publisher : Cambridge University Press
ISBN 13 : 9780521773034
Total Pages : 22 pages
Book Rating : 4.7/5 (73 download)

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Book Synopsis The Gravitational Million-Body Problem by : D. C. Heggie

Download or read book The Gravitational Million-Body Problem written by D. C. Heggie and published by Cambridge University Press. This book was released on 2003-01-23 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: The globular star clusters of the Milky Way contain hundreds of thousands of stars held together by gravitational interactions, and date from the time when the Milky Way was forming. This 2003 text describes the theory astronomers need for studying globular star clusters. The gravitational million-body problem is an idealised model for understanding the dynamics of a cluster with a million stars. After introducing the million-body problem from various view-points, the book systematically develops the tools needed for studying the million-body problems in nature, and introduces the most important theoretical models. Including a comprehensive treatment of few-body interactions, and developing an intuitive but quantitative understanding of the three-body problem, the book introduces numerical methods, relevant software, and current problems. Suitable for graduate students and researchers in astrophysics and astronomy, this text also has important applications in the fields of theoretical physics, computational science and mathematics.

Few-Body Problems in Physics ’93

Author : Bernard Becker
Publisher : Springer Science & Business Media
ISBN 13 : 3709193524
Total Pages : 503 pages
Book Rating : 4.7/5 (91 download)

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Book Synopsis Few-Body Problems in Physics ’93 by : Bernard Becker

Download or read book Few-Body Problems in Physics ’93 written by Bernard Becker and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is apparent from the history of science, that few-body problems have an interdis ciplinary character. Newton, after solving the two-body problem so brilliantly, tried his hand at the Sun-Earth-Moon system. Here he failed in two respects: neither was he able to compute the motion of the moon accurately, nor did he understand the reason for that. It took a long time to understand the fundamental importance of Newton's failure, and only Poincare realised what was the fundamental difficulty in Newtons programme. Nowadays, the term deterministic chaos is associated with this problem. The deep insights of Poincare were neglected by the founding fathers of Quantum Physics. Thus history was repeated by Bohr and his students. After quantising the hydrogen atom, they soon found that the textbook case of a three-body problem in atomic physics, the 3He-atom, did not yield to the Bohr-Sommerfeld quantisation methods. Only these days do people realise what precisely were the difficulties connected to this semi classical way of treating quantum systems. Our field, as we know it today, began in principle in the early 1950's, when Watson sketched the outlines of three-body scattering theory. Mathematical rigour was achieved by Faddeev and thereafter, at the beginning of the 1960's, the quantum three-body prob lem, at least as far as short-range forces were concerned, w&s tamed. In the years that followed, through the work of others, who first applied Faddeev's methods, but later added new techniques, the three-and four-body problems became fully housebroken.

Three Body Dynamics and Its Applications to Exoplanets

Author : Zdzislaw Musielak
Publisher : Springer
ISBN 13 : 3319582267
Total Pages : 109 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Three Body Dynamics and Its Applications to Exoplanets by : Zdzislaw Musielak

Download or read book Three Body Dynamics and Its Applications to Exoplanets written by Zdzislaw Musielak and published by Springer. This book was released on 2017-07-22 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: This brief book provides an overview of the gravitational orbital evolution of few-body systems, in particular those consisting of three bodies. The authors present the historical context that begins with the origin of the problem as defined by Newton, which was followed up by Euler, Lagrange, Laplace, and many others. Additionally, they consider the modern works from the 20th and 21st centuries that describe the development of powerful analytical methods by Poincare and others. The development of numerical tools, including modern symplectic methods, are presented as they pertain to the identification of short-term chaos and long term integrations of the orbits of many astronomical architectures such as stellar triples, planets in binaries, and single stars that host multiple exoplanets. The book includes some of the latest discoveries from the Kepler and now K2 missions, as well as applications to exoplanets discovered via the radial velocity method. Specifically, the authors give a unique perspective in relation to the discovery of planets in binary star systems and the current search for extrasolar moons.

Dynamics of Planetary Systems

Author : Scott Tremaine
Publisher : Princeton University Press
ISBN 13 : 0691244227
Total Pages : 641 pages
Book Rating : 4.6/5 (912 download)

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Book Synopsis Dynamics of Planetary Systems by : Scott Tremaine

Download or read book Dynamics of Planetary Systems written by Scott Tremaine and published by Princeton University Press. This book was released on 2023-02-07 with total page 641 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Gravitational N-Body Simulations

Author : Sverre J. Aarseth
Publisher : Cambridge University Press
ISBN 13 : 9780521432726
Total Pages : 440 pages
Book Rating : 4.4/5 (327 download)

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Book Synopsis Gravitational N-Body Simulations by : Sverre J. Aarseth

Download or read book Gravitational N-Body Simulations written by Sverre J. Aarseth and published by Cambridge University Press. This book was released on 2003-10-23 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses in detail all the relevant numerical methods for the classical N-body problem. It demonstrates how to develop clear and elegant algorithms for models of gravitational systems, and explains the fundamental mathematical tools needed to describe the dynamics of a large number of mutually attractive particles. Particular attention is given to the techniques needed to model astrophysical phenomena such as close encounters and the dynamics of black hole binaries. The author reviews relevant work in the field and covers applications to the problems of planetary formation and star cluster dynamics, both of Pleiades type and globular clusters. Self-contained and pedagogical, this book is suitable for graduate students and researchers in theoretical physics, astronomy and cosmology.

Orbital Dynamics in the Gravitational Field of Small Bodies

Author : Yang Yu
Publisher : Springer
ISBN 13 : 366252693X
Total Pages : 123 pages
Book Rating : 4.6/5 (625 download)

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Book Synopsis Orbital Dynamics in the Gravitational Field of Small Bodies by : Yang Yu

Download or read book Orbital Dynamics in the Gravitational Field of Small Bodies written by Yang Yu and published by Springer. This book was released on 2016-05-23 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: This prizewinning PhD thesis presents a general discussion of the orbital motion close to solar system small bodies (SSSBs), which induce non-central asymmetric gravitational fields in their neighborhoods. It introduces the methods of qualitative theory in nonlinear dynamics to the study of local/global behaviors around SSSBs. Detailed mechanical models are employed throughout this dissertation, and specific numeric techniques are developed to compensate for the difficulties of directly analyzing. Applying this method, several target systems, like asteroid 216 Kleopatra, are explored in great detail, and the results prove to be both revealing and pervasive for a large group of SSSBs.

Gravity, Cosmology, and Astrophysics

Author : Betti Hartmann
Publisher : Springer Nature
ISBN 13 : 3031420969
Total Pages : 321 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis Gravity, Cosmology, and Astrophysics by : Betti Hartmann

Download or read book Gravity, Cosmology, and Astrophysics written by Betti Hartmann and published by Springer Nature. This book was released on 2023-10-14 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a compilation of enlightening tutorial essays, showcasing the forefront of research by exceptional female scientists. This invaluable collection provides graduate students and researchers in the field with an engaging and pedagogical introduction to a wide range of compelling topics. Delve into the depths of theoretical and observational realms, exploring intriguing subjects including modified gravity models, quantum gravity, fields in curved space-time, particle dynamics, gravitational waves, and enigmatic black holes. Embracing both the theoretical foundations and the practical applications, this comprehensive edited volume offers an accessible and all-encompassing panorama of gravity and cosmology. Moreover, it shines a much-needed spotlight on the significant contributions made by remarkable women across the globe, fostering recognition and admiration for their indispensable role in shaping this ever-evolving field.

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

Author : B.A. Steves
Publisher : Springer Science & Business Media
ISBN 13 : 1402047061
Total Pages : 342 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Chaotic Worlds: from Order to Disorder in Gravitational N-Body Dynamical Systems by : B.A. Steves

Download or read book Chaotic Worlds: from Order to Disorder in Gravitational N-Body Dynamical Systems written by B.A. Steves and published by Springer Science & Business Media. This book was released on 2006-09-22 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Gravitational Constant: Generalized Gravitational Theories and Experiments

Author : V. de Sabbata
Publisher : Springer Science & Business Media
ISBN 13 : 1402022425
Total Pages : 432 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis The Gravitational Constant: Generalized Gravitational Theories and Experiments by : V. de Sabbata

Download or read book The Gravitational Constant: Generalized Gravitational Theories and Experiments written by V. de Sabbata and published by Springer Science & Business Media. This book was released on 2004-03-31 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date description of progress and current problems with the gravitational constant, both in terms of generalized gravitational theories and experiments either in the laboratory, using Casimir force measurements, or in space at solar system distances and in cosmological observations. Contributions cover different aspects of the state and prediction of unified theories of the physical interactions including gravitation as a cardinal link, the role of experimental gravitation and observational cosmology in discriminating between them, the problem of the precise measurement and stability of fundamental physical constants in space and time, and the gravitational constant in particular. Recent advances discussed include unified and scalar-tensor theories, theories in diverse dimensions and their observational windows, gravitational experiments in space, rotational and torsional effects in gravity, basic problems in cosmology, early universe as an arena for testing unified models, and big bang nucleosynthesis.

Dynamical Evolution of Dense Stellar Systems (IAU S246)

Author : International Astronomical Union. Symposium
Publisher : Cambridge University Press
ISBN 13 : 9780521874687
Total Pages : 516 pages
Book Rating : 4.8/5 (746 download)

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Book Synopsis Dynamical Evolution of Dense Stellar Systems (IAU S246) by : International Astronomical Union. Symposium

Download or read book Dynamical Evolution of Dense Stellar Systems (IAU S246) written by International Astronomical Union. Symposium and published by Cambridge University Press. This book was released on 2008-06-12 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dense stellar systems lie at the interface between dynamics, stellar evolution, and galaxy formation, and they provide us with an ideal laboratory to understand many different aspects of these important fields as well as to explore the interplay between them. The complete study of dense stellar systems is a very challenging task which requires the collaboration and the exchange of ideas of astronomers and physicists with observational and theoretical expertise in galactic and extra-galactic astronomy, stellar dynamics, hydrodynamics, stellar evolution, as well as knowledge of many aspects of computational physics. IAU Symposium 246 brought together experts in all these areas to cover the broad field of dense stellar systems with particular emphasis on the interplay between them and on the comparison between observations and simulations. This volume provides a complete review of the most recent studies in this topical research.

The Dynamics of Small Bodies in the Solar System

Author : B.A. Steves
Publisher : Springer Science & Business Media
ISBN 13 : 9401592217
Total Pages : 620 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis The Dynamics of Small Bodies in the Solar System by : B.A. Steves

Download or read book The Dynamics of Small Bodies in the Solar System written by B.A. Steves and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 620 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 Maratea-Acquafredda, Italy, between June 29 and July 12, 1997, entitledTHE DYNAMICS OF SMALL BODIES IN THE SOLAR SYSTEM: A MAJOR KEY TO SOLAR SYSTEM STUDIES . This Advanced Study Institute was the latest in the 'Cortina' series of NATO ASI's begun in the early 1970's firstly under the directorship of Professor Victor Szebehely and subsequently under Professor Archie Roy. All, except the latest, were held at the Antonelli Institute, Cortina d'Ampezzo, Italy. Many of those now active in the field made their first international contacts at these Institutes. The Institutes bring together many of the brightest of our young people working in dynamical astronomy, celestial mechanics and space science, enabling them to obtain an up-to-date synoptic view of their subjects delivered by lecturers of high international reputation. The proceedings from these institutes have been well-received in the internationalcommunity of research workers in the disciplines studied. The present institute included 15 series of lectures given by invited speakers and some 45 presentations made by the other participants. The majority of these contributions are includedinthese proceedings.

Gravitational N-Body Problem

Author : M. Lecar
Publisher : Springer Science & Business Media
ISBN 13 : 9401028702
Total Pages : 446 pages
Book Rating : 4.4/5 (1 download)

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Book Synopsis Gravitational N-Body Problem by : M. Lecar

Download or read book Gravitational N-Body Problem written by M. Lecar and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the third IAU conference on the Gravita tional N-Body Problem. The first IAU conference [IJ, six years ago, was motivated by the renaissance in Celestial Mechanics following the launching of artificial earth satellites, and was an attempt to bring to bear on the problems of Stellar Dynamics the sophisticated analytical techniques of Celestial Mechanics. That meeting was an outgrowth of the 'Summer Institutes in Celestial Mechanics' initiated by Dirk Brouwer. By the second IAU conference [2J, our interest had been captured by the attempts to simulate stellar systems on the computer. Computer simulation is now an essential part of stellar dynamics; journals of computational physics have started in the United Kingdom and in the United States and symposia on computer simulation of many-body problems have become a perennial event [3,4, 5]. Although our early hopes that the computer would 'solve' our problem have been tempered by experience, some techniques of computer simulation have now matured through five years of testing and use. A working description of the six most popular methods is appended to this volume. During the past three years, stellar dynamicists have followed closely the develop ments in the related field of Plasma Physics. The contexts of Plasma and Stellar Physics are deceptively similar; at first, results from Plasma Physics were bodily transferred to stellar systems by 'changing the sign of the coupling'. We are more sophisticated and more skeptical now.

Classical Newtonian Gravity

Author : Roberto A. Capuzzo Dolcetta
Publisher : Springer Nature
ISBN 13 : 3030258467
Total Pages : 176 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Classical Newtonian Gravity by : Roberto A. Capuzzo Dolcetta

Download or read book Classical Newtonian Gravity written by Roberto A. Capuzzo Dolcetta and published by Springer Nature. This book was released on 2019-09-23 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers a readily comprehensible introduction to classical Newtonian gravitation, which is fundamental for an understanding of classical mechanics and is particularly relevant to Astrophysics. The opening chapter recalls essential elements of vectorial calculus, especially to provide the formalism used in subsequent chapters. In chapter two Classical Newtonian gravity theory for one point mass and for a generic number N of point masses is then presented and discussed. The theory for point masses is naturally extended to the continuous case. The third chapter addresses the paradigmatic case of spherical symmetry in the mass density distribution (central force), with introduction of the useful tool of qualitative treatment of motion. Subsequent chapters discuss the general case of non-symmetric mass density distribution and develop classical potential theory, with elements of harmonic theory, which is essential to understand the potential development in series of the gravitational potential, the subject of the fourth chapter. Finally, in the last chapter the specific case of motion of a satellite around the earth is considered. Examples and exercises are presented throughout the book to clarify aspects of the theory. The book is aimed at those who wish to progress further beyond an initial bachelor degree, onward to a master degree, and a PhD. It is also a valuable resource for postgraduates and active researchers in the field.