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Author: June Barrow-Green Publisher: American Mathematical Soc. ISBN: 9780821803677 Category : Biography & Autobiography Languages : en Pages : 294
Book Description
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.
Author: June Barrow-Green Publisher: American Mathematical Soc. ISBN: 9780821803677 Category : Biography & Autobiography Languages : en Pages : 294
Book Description
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.
Author: Clavier Publisher: BRILL ISBN: 9004266542 Category : Religion Languages : en Pages : 440
Book Description
Preliminary Material /Henri Clavier -- Introduction Générale /Henri Clavier -- Introduction /Henri Clavier -- Quelques survivances archaïques dans les courants de la pensée biblique /Henri Clavier -- Le courant mystique et la pensée mystique. /Henri Clavier -- Le eourant prophétique dans la pensée biblique /Henri Clavier -- Le courant cultuel et la pensée biblique /Henri Clavier -- Introduction /Henri Clavier -- y A-t-il unité de pensée dans la Bible juive? /Henri Clavier -- Y A-t-il unité de pensée dsns le Nouveau Testament? /Henri Clavier -- Comment y aurait-il unité de pensée d'un Testament A L'autre ? /Henri Clavier -- L'unité au but et l'unité au centre /Henri Clavier -- Conclusion /Henri Clavier -- Index des citations bibliques /Henri Clavier -- Index des noms de lieux /Henri Clavier -- Index des noms de personnes /Henri Clavier -- Index des noms d'auteurs /Henri Clavier -- Table analytique /Henri Clavier.
Author: Luis Hernández-Lamoneda Publisher: Springer ISBN: 3319714287 Category : Mathematics Languages : en Pages : 133
Book Description
Presenting a selection of recent developments in geometrical problems inspired by the N-body problem, these lecture notes offer a variety of approaches to study them, ranging from variational to dynamical, while developing new insights, making geometrical and topological detours, and providing historical references. A. Guillot’s notes aim to describe differential equations in the complex domain, motivated by the evolution of N particles moving on the plane subject to the influence of a magnetic field. Guillot studies such differential equations using different geometric structures on complex curves (in the sense of W. Thurston) in order to find isochronicity conditions. R. Montgomery’s notes deal with a version of the planar Newtonian three-body equation. Namely, he investigates the problem of whether every free homotopy class is realized by a periodic geodesic. The solution involves geometry, dynamical systems, and the McGehee blow-up. A novelty of the approach is the use of energy-balance in order to motivate the McGehee transformation. A. Pedroza’s notes provide a brief introduction to Lagrangian Floer homology and its relation to the solution of the Arnol’d conjecture on the minimal number of non-degenerate fixed points of a Hamiltonian diffeomorphism.
Author: Victory Szebehely Publisher: Elsevier ISBN: 0323143466 Category : Science Languages : en Pages : 685
Book Description
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.
Author: C. Marchal Publisher: Elsevier ISBN: 0444600744 Category : Science Languages : en Pages : 593
Book Description
Recent research on the theory of perturbations, the analytical approach and the quantitative analysis of the three-body problem have reached a high degree of perfection. The use of electronics has aided developments in quantitative analysis and has helped to disclose the extreme complexity of the set of solutions. This accelerated progress has given new orientation and impetus to the qualitative analysis that is so complementary to the quantitative analysis. The book begins with the various formulations of the three-body problem, the main classical results and the important questions and conjectures involved in this subject. The main part of the book describes the remarkable progress achieved in qualitative analysis which has shed new light on the three-body problem. It deals with questions such as escapes, captures, periodic orbits, stability, chaotic motions, Arnold diffusion, etc. The most recent tests of escape have yielded very impressive results and border very close on the true limits of escape, showing the domain of bounded motions to be much smaller than was expected. An entirely new picture of the three-body problem is emerging, and the book reports on this recent progress. The structure of the solutions for the three-body problem lead to a general conjecture governing the picture of solutions for all Hamiltonian problems. The periodic, quasi-periodic and almost-periodic solutions form the basis for the set of solutions and separate the chaotic solutions from the open solutions.
Author: L. G. Napolitano Publisher: Elsevier ISBN: 1483159914 Category : Technology & Engineering Languages : en Pages : 496
Book Description
Space and Energy contains the proceedings of the 26th Congress of the International Astronautical Federation, held in Lisbon, Portugal, on September 21-27, 1975. The papers explore developments and trends of interest as well as research in space and energy. Topics covered range from engineering and life sciences to space systems, space technology, and communication satellites. This book is comprised of 16 chapters and begins with a discussion on the Earth as an open system and how to utilize solar energy. The next section is devoted to engineering and life sciences and includes chapters giving surveys and/or assessments of a number of basic topics in astrodynamics and bioastronautics. Propulsion system concepts for a single stage shuttle are also considered, along with the reliability of outer planet spacecraft and the contribution of biological satellites to space biology and medicine. Specific systems such as an experimental hybrid rocket are also described. The last part evaluates application satellites, with particular reference to communication and earth resource satellites. This monograph should be of interest to space scientists and engineers.
Author: Paolo Freguglia Publisher: Birkhäuser ISBN: 3319389459 Category : Mathematics Languages : en Pages : 297
Book Description
This monograph explores the early development of the calculus of variations in continental Europe during the Eighteenth Century by illustrating the mathematics of its founders. Closely following the original papers and correspondences of Euler, Lagrange, the Bernoullis, and others, the reader is immersed in the challenge of theory building. We see what the founders were doing, the difficulties they faced, the mistakes they made, and their triumphs. The authors guide the reader through these works with instructive commentaries and complements to the original proofs, as well as offering a modern perspective where useful. The authors begin in 1697 with Johann Bernoulli’s work on the brachystochrone problem and the events leading up to it, marking the dawn of the calculus of variations. From there, they cover key advances in the theory up to the development of Lagrange’s δ-calculus, including: • The isoperimetrical problems • Shortest lines and geodesics • Euler’s Methodus Inveniendi and the two Additamenta Finally, the authors give the readers a sense of how vast the calculus of variations has become in centuries hence, providing some idea of what lies outside the scope of the book as well as the current state of affairs in the field. This book will be of interest to anyone studying the calculus of variations who wants a deeper intuition for the techniques and ideas that are used, as well as historians of science and mathematics interested in the development and evolution of modern calculus and analysis.
Author: June Barrow-Green
Author: June Barrow-Green
Author: Clavier
Author: Luis Hernández-Lamoneda
Author: Victory Szebehely
Author: Royal Society (Great Britain)
Author: Royal Society (Great Britain)
Author: C. Marchal
Author: Pierre Simon marquis de Laplace
Author: L. G. Napolitano
Author: Paolo Freguglia