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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: 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: Daniel Benest Publisher: Springer ISBN: 3540480099 Category : Science Languages : en Pages : 226
Book Description
Chaos theory plays an important role in modern physics and related sciences, but -, the most important results so far have been obtained in the study of gravitational systems applied to celestial mechanics. The present set of lectures introduces the mathematical methods used in the theory of singularities in gravitational systems, reviews modeling techniques for the simulation of close encounters and presents the state of the art about the study of diffusion of comets, wandering asteroids, meteors and planetary ring particles. The book will be of use to researchers and graduate students alike.
Author: Craig A. Stephenson Publisher: American Mathematical Soc. ISBN: 1470456710 Category : Education Languages : en Pages : 255
Book Description
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.
Author: Alexander D. Bruno Publisher: Walter de Gruyter ISBN: 3110901730 Category : Mathematics Languages : en Pages : 377
Book Description
The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany
Author: Vladimir I. Arnol'd Publisher: Springer Science & Business Media ISBN: 3662025353 Category : Science Languages : en Pages : 305
Book Description
This work describes the fundamental principles, problems, and methods of elassical mechanics focussing on its mathematical aspects. The authors have striven to give an exposition stressing the working apparatus of elassical mechanics, rather than its physical foundations or applications. This appara tus is basically contained in Chapters 1, 3,4 and 5. Chapter 1 is devoted to the fundamental mathematical models which are usually employed to describe the motion of real mechanical systems. Special consideration is given to the study of motion under constraints, and also to problems concerned with the realization of constraints in dynamics. Chapter 3 is concerned with the symmetry groups of mechanical systems and the corresponding conservation laws. Also discussed are various aspects of the theory of the reduction of order for systems with symmetry, often used in applications. Chapter 4 contains abrief survey of various approaches to the problem of the integrability of the equations of motion, and discusses some of the most general and effective methods of integrating these equations. Various elassical examples of integrated problems are outlined. The material pre sen ted in this chapter is used in Chapter 5, which is devoted to one of the most fruitful branches of mechanics - perturbation theory. The main task of perturbation theory is the investigation of problems of mechanics which are" elose" to exact1y integrable problems.
Author: Arthur Beer Publisher: Elsevier ISBN: 1483225135 Category : Science Languages : en Pages : 793
Book Description
Vistas in Astronomy, Volume 1: Co-operation and Organization, History and Philosophy, Dynamics, Theoretical Astrophysics, Instruments, Radio Astronomy, Solar Physics brings together the ideas that form the structural units of what is known about astronomy. This book is organized into seven sections encompassing 93 chapters. Section I provides a summary of the significant contributions of international cooperation and various astronomy-related organizations in the advancement of astronomy. Section II highlights the historical developments in astronomy, from the early studies of the Egyptians to the formulation of philosophical concepts of cosmology. Sections III and IV describes the dynamic and theoretical aspects of astrophysics. These sections consider research studies on stellar dynamics, atmospheres, and magnetic fields, as well as the formation of condensation in a gaseous nebula. Part V is devoted o the developments in telescope optics and mirrors, spectrographs, electronic calculating machines, and photometers, while Section VI examines the field of radio astronomy. Part VII looks into solar physics related studies, including the structure and movements of sunspots, eclipse observation, and spectroscopic investigations of the solar corona. This book is of great value to astronomers, astrophysicists, solar physicists, and researchers in the allied fields.
Author: June Barrow-Green
Author: June Barrow-Green
Author: Carl Ludwig Siegel
Author: C. Marchal
Author: Daniel Benest
Author: Craig A. Stephenson
Author: Alexander D. Bruno
Author: Vladimir I. Arnol'd
Author: 
Author: National Science Foundation (U.S.)
Author: Arthur Beer