On Poincar S Non Existence Of Integrals For The Three Body Problem
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On Poincar S Non Existence Of Integrals For The Three Body Problem
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Author : Stephen Peter Diliberto
language : en
Publisher:
Release Date : 1970
On Poincar S Non Existence Of Integrals For The Three Body Problem written by Stephen Peter Diliberto and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Three-body problem categories.
The author's results on difference equations are applied to produce a new type of proof for Poincare's non-exstence theorem. The new proof/method avoids cirticisms of all earlier proofs.
Poincare And The Three Body Problem
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Author : June Barrow-Green
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Poincare And The Three Body Problem written by June Barrow-Green and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Biography & Autobiography categories.
Poincare's famous memoir on the three body problem arose from his entry in the competition celebrating the 60th birthday of King Oscar of Sweden and Norway. His essay won the prize and was set up in print as a paper in Acta Mathematica when it was found to contain a deep and critical error. In correcting this error Poincare discovered mathematical chaos, as is now clear from June Barrow-Green's pioneering study of a copy of the original memoir annotated by Poincare himself, recently discovered in the Institut Mittag-Leffler in Stockholm. Poincare and the Three Body Problem opens with a discussion of the development of the three body problem itself and Poincare's related earlier work. The book also contains intriguing insights into the contemporary European mathematical community revealed by the workings of the competition. After an account of the discovery of the error and a detailed comparative study of both the original memoir and its rewritten version, the book concludes with an account of the final memoir's reception, influence and impact, and an examination of Poincare's subsequent highly influential work in celestial mechanics.
Landmark Writings In Western Mathematics 1640 1940
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Author : Ivor Grattan-Guinness
language : en
Publisher: Elsevier
Release Date : 2005-02-11
Landmark Writings In Western Mathematics 1640 1940 written by Ivor Grattan-Guinness and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-02-11 with Mathematics categories.
This book contains around 80 articles on major writings in mathematics published between 1640 and 1940. All aspects of mathematics are covered: pure and applied, probability and statistics, foundations and philosophy. Sometimes two writings from the same period and the same subject are taken together. The biography of the author(s) is recorded, and the circumstances of the preparation of the writing are given. When the writing is of some lengths an analytical table of its contents is supplied. The contents of the writing is reviewed, and its impact described, at least for the immediate decades. Each article ends with a bibliography of primary and secondary items. First book of its kind Covers the period 1640-1940 of massive development in mathematics Describes many of the main writings of mathematics Articles written by specialists in their field
Periodic Orbits F R Moulton S Quest For A New Lunar Theory
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Author : Craig A. Stephenson
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-05-19
Periodic Orbits F R Moulton S Quest For A New Lunar Theory written by Craig A. Stephenson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-19 with Education categories.
Owing to its simple formulation and intractable nature, along with its application to the lunar theory, the three-body problem has since it was first studied by Newton in the Principia attracted the attention of many of the world's most gifted mathematicians and astronomers. Two of these, Euler and Lagrange, discovered the problem's first periodic solutions. However, it was not until Hill's discovery in the late 1870s of the variational orbit that the importance of the periodic solutions was fully recognized, most notably by Poincaré, but also by others such as Sir George Darwin. The book begins with a detailed description of the early history of the three-body problem and its periodic solutions, with chapters dedicated to the pioneering work of Hill, Poincaré, and Darwin. This is followed by the first in-depth account of the contribution to the subject by the mathematical astronomer Forest Ray Moulton and his research students at the University of Chicago. The author reveals how Moulton's Periodic Orbits, published in 1920 and running to some 500 pages, arose from Moulton's ambitious goal of creating an entirely new lunar theory. The methods Moulton developed in the pursuit of this goal are described and an examination is made of both the reception of his work and his legacy for future generations of researchers.
Henri Poincar 1912 2012
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Author : Bertrand Duplantier
language : en
Publisher: Springer
Release Date : 2014-11-14
Henri Poincar 1912 2012 written by Bertrand Duplantier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-14 with Mathematics categories.
This thirteenth volume of the Poincaré Seminar Series, Henri Poincaré, 1912-2012, is published on the occasion of the centennial of the death of Henri Poincaré in 1912. It presents a scholarly approach to Poincaré’s genius and creativity in mathematical physics and mathematics. Its five articles are also highly pedagogical, as befits their origin in lectures to a broad scientific audience. Highlights include “Poincaré’s Light” by Olivier Darrigol, a leading historian of science, who uses light as a guiding thread through much of Poincaré ’s physics and philosophy, from the application of his superior mathematical skills and the theory of diffraction to his subsequent reflections on the foundations of electromagnetism and the electrodynamics of moving bodies; the authoritative “Poincaré and the Three-Body Problem” by Alain Chenciner, who offers an exquisitely detailed, hundred-page perspective, peppered with vivid excerpts from citations, on the monumental work of Poincaré on this subject, from the famous (King Oscar’s) 1889 memoir to the foundations of the modern theory of chaos in “Les méthodes nouvelles de la mécanique céleste.” A profoundly original and scholarly presentation of the work by Poincaré on probability theory is given by Laurent Mazliak in “Poincaré’s Odds,” from the incidental first appearance of the word “probability” in Poincaré’s famous 1890 theorem of recurrence for dynamical systems, to his later acceptance of the unavoidability of probability calculus in Science, as developed to a great extent by Emile Borel, Poincaré’s main direct disciple; the article by Francois Béguin, “Henri Poincaré and the Uniformization of Riemann Surfaces,” takes us on a fascinating journey through the six successive versions in twenty-six years of the celebrated uniformization theorem, which exemplifies the Master’s distinctive signature in the foundational fusion of mathematics and physics, on which conformal field theory, string theory and quantum gravity so much depend nowadays; the final chapter, “Harmony and Chaos, On the Figure of Henri Poincaré” by the filmmaker Philippe Worms, describes the homonymous poetical film in which eminent scientists, through mathematical scenes and physical experiments, display their emotional relationship to the often elusive scientific truth and universal “harmony and chaos” in Poincaré’s legacy. This book will be of broad general interest to physicists, mathematicians, philosophers of science and historians.
From Eudoxus To Einstein
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Author : C. M. Linton
language : en
Publisher: Cambridge University Press
Release Date : 2004-08-12
From Eudoxus To Einstein written by C. M. Linton and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-08-12 with Science categories.
Since man first looked towards the heavens, a great deal of effort has been put into trying to predict and explain the motions of the sun, moon and planets. Developments in man's understanding have been closely linked to progress in the mathematical sciences. Whole new areas of mathematics, such as trigonometry, were developed to aid astronomical calculations, and on numerous occasions throughout history, breakthroughs in astronomy have only been possible because of progress in mathematics. This book describes the theories of planetary motion that have been developed through the ages, beginning with the homocentric spheres of Eudoxus and ending with Einstein's general theory of relativity. It emphasizes the interaction between progress in astronomy and in mathematics, showing how the two have been inextricably linked since Babylonian times. This valuable text is accessible to a wide audience, from amateur astronomers to professional historians of astronomy.
The Genesis Of Simulation In Dynamics
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Author : Thomas P. Weissert
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Genesis Of Simulation In Dynamics written by Thomas P. Weissert and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
An introduction to certain aspects of developments in the modern theory of dynamics and simulation for a wide audience of scientifically literate readers. Unlike general texts on chaos theory and dynamical systems theory, this book follows the work on a specific problem at the very beginning of the modern era of dynamics, from its inception in 1954 through the early 1970s. It discusses such problems as the nonlinear oscillator simulation, the seminal discoveries at MIT in the early 1950s, the mathematical rediscovery of solitons in the late 1950s and the general problems of computability. In following these developments, the initial development of many of the now standard techniques of nonlinear modelling and numerical simulation are seen. No other text focuses so tightly and covers so completely one specific, pernicious problem at the heart of dynamics.
Theory Of Orbit
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Author : Victory Szebehely
language : en
Publisher: Elsevier
Release Date : 2012-12-02
Theory Of Orbit written by Victory Szebehely and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Science categories.
Theory of Orbits: The Restricted Problem of Three Bodies is a 10-chapter text that covers the significance of the restricted problem of three bodies in analytical dynamics, celestial mechanics, and space dynamics. The introductory part looks into the use of three essentially different approaches to dynamics, namely, the qualitative, the quantitative, and the formalistic. The opening chapters consider the formulation of equations of motion in inertial and in rotating coordinate systems, as well as the reductions of the problem of three bodies and the corresponding streamline analogies. These topics are followed by discussions on the regularization and writing of equations of motion in a singularity-free systems; the principal qualitative aspect of the restricted problem of the curves of zero velocity; and the motion and nonlinear stability in the neighborhood of libration points. This text further explores the principles of Hamiltonian dynamics and its application to the restricted problem in the extended phase space. A chapter treats the problem of two bodies in a rotating coordinate system and treats periodic orbits in the restricted problem. Another chapter focuses on the comparison of the lunar and interplanetary orbits in the Soviet and American literature. The concluding chapter is devoted to modifications of the restricted problem, such as the elliptic, three-dimensional, and Hill’s problem. This book is an invaluable source for astronomers, engineers, and mathematicians.
Vladimir I Arnold Collected Works
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Author : Vladimir I. Arnold
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-11
Vladimir I Arnold Collected Works written by Vladimir I. Arnold and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Mathematics categories.
Vladimir Arnold was one of the great mathematical scientists of our time. He is famous for both the breadth and the depth of his work. At the same time he is one of the most prolific and outstanding mathematical authors. This second volume of his Collected Works focuses on hydrodynamics, bifurcation theory, and algebraic geometry.
Three Body Dynamics And Its Applications To Exoplanets
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Author : Zdzislaw Musielak
language : en
Publisher: Springer
Release Date : 2017-07-22
Three Body Dynamics And Its Applications To Exoplanets written by Zdzislaw Musielak and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-22 with Science categories.
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.