Search results for: numerical-solutions-of-the-n-body-problem

Numerical Solutions of the N Body Problem

Author : A. Marciniak
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Approach your problem from the right It isn't that they can't see end and begin with the answers. the solution. Then one day, perhaps you will find It is that they can't see the the final question. problem. G.K. Chesterton. The Scandal The Hermit Clad in Crane Feathers in of Father Brown The Point of R. van Gulik's The Chinese Maze Murders. a Pin. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new brancheq. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics, algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisci fI plines as "experimental mathematics", "CFD , "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes.

Chaos in Gravitational N Body Systems

Author : J.C. Muzzio
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The Workshop on Chaos in Gravitational N -Body Systems was held in La Plata, Argentina, from July 31 through August 3, 1995. The School of Astronomy and Geophysics of La Plata National University, best known as La Plata Observatory, was the host institution. The Observatory (cover photo) was founded in 1883, and it has nowadays about 120 faculty members and 70 non-faculty members devoted to teaching and research in different areas of astronomy and geophysics. It was very nice to see how many people, from young students to well recognized authorities in the field, came to participate in the meeting. This audience success was due to the increasing understanding of the neces sity to gather together people from Celestial Mechanics and Stellar Dynamics to explore the problems that exist at the frontier of these two disciplines and their common interest in chaotic phenomena and integrability (the famous Argentine beef was, certainly, also an attraction!). All the papers of the present volume were refereed. Most were accepted after some revision, while some needed no change at all (compli ments to their authors!) and, sadly, a few could not be included. About half a dozen authors did not submit their contributions for publication, mainly because they were already in print elsewhere. Therefore, the special issue of Celestial Mechanics and Dynamical Astronomy includes all the invited lectures of the workshop, while the proceedings volume includes those same lectures plus the bulk of, but Bot all, the contributions to the meeting.

Periodic Solutions of the N Body Problem

Author : Kenneth R. Meyer
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The N-body problem is the classical prototype of a Hamiltonian system with a large symmetry group and many first integrals. These lecture notes are an introduction to the theory of periodic solutions of such Hamiltonian systems. From a generic point of view the N-body problem is highly degenerate. It is invariant under the symmetry group of Euclidean motions and admits linear momentum, angular momentum and energy as integrals. Therefore, the integrals and symmetries must be confronted head on, which leads to the definition of the reduced space where all the known integrals and symmetries have been eliminated. It is on the reduced space that one can hope for a nonsingular Jacobian without imposing extra symmetries. These lecture notes are intended for graduate students and researchers in mathematics or celestial mechanics with some knowledge of the theory of ODE or dynamical system theory. The first six chapters develops the theory of Hamiltonian systems, symplectic transformations and coordinates, periodic solutions and their multipliers, symplectic scaling, the reduced space etc. The remaining six chapters contain theorems which establish the existence of periodic solutions of the N-body problem on the reduced space.

Gravitational N Body Problem

Author : M. Lecar
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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.

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

Author : Bonnie Steves
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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

Gravitational N Body Simulations

Author : Sverre J. Aarseth
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Unique coverage of subject, including the mathematics for computational methods of the classical N-body problem.

Atmospheric and Space Flight Dynamics

Author : Ashish Tewari
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This book offers a unified presentation that does not discriminate between atmospheric and space flight. It demonstrates that the two disciplines have evolved from the same set of physical principles and introduces a broad range of critical concepts in an accessible, yet mathematically rigorous presentation. The book presents many MATLAB and Simulink-based numerical examples and real-world simulations. Replete with illustrations, end-of-chapter exercises, and selected solutions, the work is primarily useful as a textbook for advanced undergraduate and beginning graduate-level students.

The Three Body Problem

Author : Valtonen. M. J. (Mauri J.)
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"How do three celestial bodies move under their mutual gravitational attraction? It is a problem that has been studied by Isaac Newton and leading mathematicians over the last two centuries. Poincare's conclusion that the problem represents an example ofchaos in nature, opens new possibilities of dealing with it: a statistical approach. For the first time such methods are presented in a systematic way. The book surveys statistical methods as well as more traditional methods, suitable for students of celestial mechanics at advanced undergraduate level."--BOOK JACKET.

The N body Code

Author : William C. Strack
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The Few Body Problem

Author : Mauri Valtonen
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th Coinciding with the 300 anniversary of the publication of Newton's Principia The International Astronomical Union organized the colloquium No. 96 "The Few Body Problem" in Turku, Finland, June 14.-19.1987. It provided an opportunity to review the progress in the very field which caused Newton a headache, as Victor Szebehely reminded the audience in his introductory remarks. It is a measure of the difficulty and complication of the few body problem that even after 300 years so many aspects of the problem are still unsolved. To quote Szebehely again, "Sir Isaac established the rules, Poincare presented the challenges". Many of these challenges are reviewed in the present proceedings. The gravitational few body problem cuts across the borders of established disciplines. The participants of the colloquium came from departments as different as Aerospace Engineering, Astronomy, Theoretical Physics, Physics, Mathematics, Applied Mathematics, Computer Science, Planetology, Geodesy, Celestial Mechanics and Space Science. The few body problem is a problem of practical significance in many fields and the main aim of the colloquium was to bring together people with research interests in this area, many of whom normally attend different conferences.

Introduction to Parallel Computing

Author : Roman Trobec
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Advancements in microprocessor architecture, interconnection technology, and software development have fueled rapid growth in parallel and distributed computing. However, this development is only of practical benefit if it is accompanied by progress in the design, analysis and programming of parallel algorithms. This concise textbook provides, in one place, three mainstream parallelization approaches, Open MPP, MPI and OpenCL, for multicore computers, interconnected computers and graphical processing units. An overview of practical parallel computing and principles will enable the reader to design efficient parallel programs for solving various computational problems on state-of-the-art personal computers and computing clusters. Topics covered range from parallel algorithms, programming tools, OpenMP, MPI and OpenCL, followed by experimental measurements of parallel programs’ run-times, and by engineering analysis of obtained results for improved parallel execution performances. Many examples and exercises support the exposition.

N body Problems and Models

Author : Donald Greenspan
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The study and application of N-body problems has had an important role in the history of mathematics. In recent years, the availability of modern computer technology has added to their significance, since computers can now be used to model material bodies as atomic and molecular configurations, i.e. as N-body configurations.This book can serve either as a handbook or as a text. Methodology, intuition, and applications are interwoven throughout. Nonlinearity and determinism are emphasized. The book can be used on any level provided that the reader has at least some ability with numerical methodology, computer programming, and basic physics. It will be of interest to mathematicians, engineers, computer scientists, physicists, chemists, and biologists.Some unique features of the book include: (1) development of turbulent flow which is consistent with experimentation, unlike any continuum model; (2) applicability to rotating tops with nonuniform density; (3) conservative methodology which conserves the same energy and momentum as continuous systems.

Introduction to Hamiltonian Dynamical Systems and the N Body Problem

Author : Kenneth R. Meyer
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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)

Astronomical Observations Astronomy and the Study of Deep Space

Author : Britannica Educational Publishing
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The night sky is positively teeming with wonders, from star clusters and nebulae to quasars. Astronomy is the means by which these and other similar phenomena are discovered and observed. This stellar resource traces the path of modern astronomy, from initial efforts to map the heavens to today’s use of high-tech telescopic devices that help people delve deeper into celestial discovery.

Predictability Stability and Chaos in N Body Dynamical Systems

Author : Archie E. Roy
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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.

Applied Mechanics Reviews

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Intelligent Computing

Author : Kohei Arai
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This book presents the proceedings of the Computing Conference 2019, providing a comprehensive collection of chapters focusing on core areas of computing and their real-world applications. Computing is an extremely broad discipline, encompassing a range of specialized fields, each focusing on particular areas of technology and types of application, and the conference offered pioneering researchers, scientists, industrial engineers, and students from around the globe a platform to share new ideas and development experiences. Providing state-of-the-art intelligent methods and techniques for solving real- world problems, the book inspires further research and technological advances in this important area.

Proceedings of the Conference on the Numerical Solution of Ordinary Differential Equations

Author : D.G. Bettis
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Numerical Solution of Ordinary Differential Equations

Author : Donald Greenspan
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This work meets the need for an affordable textbook that helps in understanding numerical solutions of ODE. Carefully structured by an experienced textbook author, it provides a survey of ODE for various applications, both classical and modern, including such special applications as relativistic systems. The examples are carefully explained and compiled into an algorithm, each of which is presented independent of a specific programming language. Each chapter is rounded off with exercises.

Methods of Celestial Mechanics

Author : Gerhard Beutler
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G. Beutler's Methods of Celestial Mechanics is a coherent textbook for students as well as an excellent reference for practitioners. The first volume gives a thorough treatment of celestial mechanics and presents all the necessary mathematical details that a professional would need. The reader will appreciate the well-written chapters on numerical solution techniques for ordinary differential equations, as well as that on orbit determination. In the second volume applications to the rotation of earth and moon, to artificial earth satellites and to the planetary system are presented. The author addresses all aspects that are of importance in high-tech applications, such as the detailed gravitational fields of all planets and the earth, the oblateness of the earth, the radiation pressure and the atmospheric drag. The concluding part of this monumental treatise explains and details state-of-the-art professional and thoroughly-tested software for celestial mechanics.