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N Body Problems And Gravitational Dynamics
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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.
Book Synopsis Introduction to Hamiltonian Dynamical Systems and the N-Body Problem by : Kenneth R. Meyer
Download or read book Introduction to Hamiltonian Dynamical Systems and the N-Body Problem written by Kenneth R. Meyer and published by Springer. This book was released on 2017-05-04 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This third edition text provides expanded material on the restricted three body problem and celestial mechanics. With each chapter containing new content, readers are provided with new material on reduction, orbifolds, and the regularization of the Kepler problem, all of which are provided with applications. The previous editions grew out of graduate level courses in mathematics, engineering, and physics given at several different universities. The courses took students who had some background in differential equations and lead them through a systematic grounding in the theory of Hamiltonian mechanics from a dynamical systems point of view. This text provides a mathematical structure of celestial mechanics ideal for beginners, and will be useful to graduate students and researchers alike. Reviews of the second edition: "The primary subject here is the basic theory of Hamiltonian differential equations studied from the perspective of differential dynamical systems. The N-body problem is used as the primary example of a Hamiltonian system, a touchstone for the theory as the authors develop it. This book is intended to support a first course at the graduate level for mathematics and engineering students. ... It is a well-organized and accessible introduction to the subject ... . This is an attractive book ... ." (William J. Satzer, The Mathematical Association of America, March, 2009) “The second edition of this text infuses new mathematical substance and relevance into an already modern classic ... and is sure to excite future generations of readers. ... This outstanding book can be used not only as an introductory course at the graduate level in mathematics, but also as course material for engineering graduate students. ... it is an elegant and invaluable reference for mathematicians and scientists with an interest in classical and celestial mechanics, astrodynamics, physics, biology, and related fields.” (Marian Gidea, Mathematical Reviews, Issue 2010 d)
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 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents basic methods for numerical simulation of gravitational systems, demonstrating how to develop clear and elegant algorithms. It explains the fundamental mathematical tools needed to describe the dynamics of a large number of mutually attractive particles, and the techniques needed to model various known planetary and astrophysical phenomena.
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.
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
Book Synopsis N-body Problems and Gravitational Dynamics by : F. Combes
Download or read book N-body Problems and Gravitational Dynamics written by F. Combes and published by . This book was released on 1993 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Hamiltonian Dynamical Systems and the N-Body Problem by : Kenneth Meyer
Download or read book Introduction to Hamiltonian Dynamical Systems and the N-Body Problem written by Kenneth Meyer and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of Hamiltonian systems is a vast subject which can be studied from many different viewpoints. This book develops the basic theory of Hamiltonian differential equations from a dynamical systems point of view. That is, the solutions of the differential equations are thought of as curves in a phase space and it is the geometry of these curves that is the important object of study. The analytic underpinnings of the subject are developed in detail. The last chapter on twist maps has a more geometric flavor. It was written by Glen R. Hall. The main example developed in the text is the classical N-body problem, i.e., the Hamiltonian system of differential equations which describe the motion of N point masses moving under the influence of their mutual gravitational attraction. Many of the general concepts are applied to this example. But this is not a book about the N-body problem for its own sake. The N-body problem is a subject in its own right which would require a sizable volume of its own. Very few of the special results which only apply to the N-body problem are given.
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.
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 Applied General Relativity by : Michael H. Soffel
Download or read book Applied General Relativity written by Michael H. Soffel and published by Springer Nature. This book was released on 2019-09-23 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the late 20th and beginning 21st century high-precision astronomy, positioning and metrology strongly rely on general relativity. Supported by exercises and solutions this book offers graduate students and researchers entering those fields a self-contained and exhaustive but accessible treatment of applied general relativity. The book is written in a homogenous (graduate level textbook) style allowing the reader to understand the arguments step by step. It first introduces the mathematical and theoretical foundations of gravity theory and then concentrates on its general relativistic applications: clock rates, clock sychronization, establishment of time scales, astronomical references frames, relativistic astrometry, celestial mechanics and metrology. The authors present up-to-date relativistic models for applied techniques such as Satellite LASER Ranging (SLR), Lunar LASER Ranging (LLR), Globale Navigation Satellite Systems (GNSS), Very Large Baseline Interferometry (VLBI), radar measurements, gyroscopes and pulsar timing. A list of acronyms helps the reader keep an overview and a mathematical appendix provides required functions and terms.
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.
Book Synopsis Dynamical Systems by : Wang Sang Koon
Download or read book Dynamical Systems written by Wang Sang Koon and published by Springer. This book was released on 2011-06-01 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book considers global solutions to the restricted three-body problem from a geometric point of view. The authors seek dynamical channels in the phase space which wind around the planets and moons and naturally connect them. These low energy passageways could slash the amount of fuel spacecraft need to explore and develop our solar system. In order to effectively exploit these passageways, the book addresses the global transport. It goes beyond the traditional scope of libration point mission design, developing tools for the design of trajectories which take full advantage of natural three or more body dynamics, thereby saving precious fuel and gaining flexibility in mission planning. This is the key for the development of some NASA mission trajectories, such as low energy libration point orbit missions (e.g., the sample return Genesis Discovery Mission), low energy lunar missions and low energy tours of outer planet moon systems, such as a mission to tour and explore in detail the icy moons of Jupiter. This book can serve as a valuable resource for graduate students and advanced undergraduates in applied mathematics and aerospace engineering, as well as a manual for practitioners who work on libration point and deep space missions in industry and at government laboratories. the authors include a wealth of background material, but also bring the reader up to a portion of the research frontier.
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 . This book was released on 2003 with total page 430 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.
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.
Book Synopsis Orbital Mechanics for Engineering Students by : Howard D Curtis
Download or read book Orbital Mechanics for Engineering Students written by Howard D Curtis and published by Elsevier. This book was released on 2009-10-26 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt: Orbital Mechanics for Engineering Students, Second Edition, provides an introduction to the basic concepts of space mechanics. These include vector kinematics in three dimensions; Newton’s laws of motion and gravitation; relative motion; the vector-based solution of the classical two-body problem; derivation of Kepler’s equations; orbits in three dimensions; preliminary orbit determination; and orbital maneuvers. The book also covers relative motion and the two-impulse rendezvous problem; interplanetary mission design using patched conics; rigid-body dynamics used to characterize the attitude of a space vehicle; satellite attitude dynamics; and the characteristics and design of multi-stage launch vehicles. Each chapter begins with an outline of key concepts and concludes with problems that are based on the material covered. This text is written for undergraduates who are studying orbital mechanics for the first time and have completed courses in physics, dynamics, and mathematics, including differential equations and applied linear algebra. Graduate students, researchers, and experienced practitioners will also find useful review materials in the book. NEW: Reorganized and improved discusions of coordinate systems, new discussion on perturbations and quarternions NEW: Increased coverage of attitude dynamics, including new Matlab algorithms and examples in chapter 10 New examples and homework problems
Book Synopsis Astrophysical Recipes by : Simon Portegies Zwart
Download or read book Astrophysical Recipes written by Simon Portegies Zwart and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Computational astrophysics is a new and quickly growing discipline. In this book the authors outline the fundamentals for computational astrophysics, focusing on the use of the Astronomical Multipurpose Software Environment (AMUSE), which is a general-purpose simulation environment in astrophysics written in Python. AMUSE allows you to combine existing solvers to build new applications that can be combined again to study gradually more complex situations. This enables the growth of multi-physics and multi-scale application software in a hierarchical fashion, testing each intermediate step as the complexity of the software continues to increase. All examples in the book are associated with codes that run on a simple laptop or workstation. All figures are reproducible with a simple script, and all scripts are available online to be downloaded and run accordingly."--Source : résumé de l'éditeur.
Book Synopsis Simulating Hamiltonian Dynamics by : Benedict Leimkuhler
Download or read book Simulating Hamiltonian Dynamics written by Benedict Leimkuhler and published by Cambridge University Press. This book was released on 2004 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric integrators are time-stepping methods, designed such that they exactly satisfy conservation laws, symmetries or symplectic properties of a system of differential equations. In this book the authors outline the principles of geometric integration and demonstrate how they can be applied to provide efficient numerical methods for simulating conservative models. Beginning from basic principles and continuing with discussions regarding the advantageous properties of such schemes, the book introduces methods for the N-body problem, systems with holonomic constraints, and rigid bodies. More advanced topics treated include high-order and variable stepsize methods, schemes for treating problems involving multiple time-scales, and applications to molecular dynamics and partial differential equations. The emphasis is on providing a unified theoretical framework as well as a practical guide for users. The inclusion of examples, background material and exercises enhance the usefulness of the book for self-instruction or as a text for a graduate course on the subject.
