Poincare and the Three Body Problem

Poincare and the Three Body Problem PDF

Author: June Barrow-Green

Publisher: American Mathematical Soc.

Published: 1997

Total Pages: 294

ISBN-13: 9780821803677

DOWNLOAD EBOOK →

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.

The Three-Body Problem and the Equations of Dynamics

The Three-Body Problem and the Equations of Dynamics PDF

Author: Henri Poincaré

Publisher: Springer

Published: 2017-05-11

Total Pages: 265

ISBN-13: 3319528998

DOWNLOAD EBOOK →

Here is an accurate and readable translation of a seminal article by Henri Poincaré that is a classic in the study of dynamical systems popularly called chaos theory. In an effort to understand the stability of orbits in the solar system, Poincaré applied a Hamiltonian formulation to the equations of planetary motion and studied these differential equations in the limited case of three bodies to arrive at properties of the equations’ solutions, such as orbital resonances and horseshoe orbits. Poincaré wrote for professional mathematicians and astronomers interested in celestial mechanics and differential equations. Contemporary historians of math or science and researchers in dynamical systems and planetary motion with an interest in the origin or history of their field will find his work fascinating.

Galileo Unbound

Galileo Unbound PDF

Author: David D. Nolte

Publisher: Oxford University Press

Published: 2018-07-12

Total Pages: 384

ISBN-13: 0192528505

DOWNLOAD EBOOK →

Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.

The Three-Body Problem

The Three-Body Problem PDF

Author: Mauri J. Valtonen

Publisher: Cambridge University Press

Published: 2006-03-02

Total Pages: 366

ISBN-13: 9780521852241

DOWNLOAD EBOOK →

How do three celestial bodies move under their mutual gravitational attraction? This problem has been studied by Isaac Newton and leading mathematicians over the last two centuries. Poincaré's conclusion, that the problem represents an example of chaos in nature, opens the new possibility of using a statistical approach. For the first time this book presents these methods in a systematic way, surveying statistical as well as more traditional methods. The book begins by providing an introduction to celestial mechanics, including Lagrangian and Hamiltonian methods, and both the two and restricted three body problems. It then surveys statistical and perturbation methods for the solution of the general three body problem, providing solutions based on combining orbit calculations with semi-analytic methods for the first time. This book should be essential reading for students in this rapidly expanding field and is suitable for students of celestial mechanics at advanced undergraduate and graduate level.

The Three-Body Problem

The Three-Body Problem PDF

Author: Catherine Shaw

Publisher: Allison & Busby

Published: 2013-05-27

Total Pages: 277

ISBN-13: 074901444X

DOWNLOAD EBOOK →

Cambridge, 1888. When schoolmistress Vanessa Duncan learns of a murder at St John's College, little does she know that she will become deeply entangled in the mystery. Dr Geoffrey Akers, Fellow in Pure Mathematics, has been found dead, struck down by a violent blow to the head. What could provoke such a brutal act? Vanessa, finding herself in amongst Cambridge's brightest scholarly minds, discovers that the motive may lie in mathematics itself. Drawn closer to the case by a blossoming friendship with mathematician Arthur Weatherburn, Vanessa begins to investigate. When she learns of Sir Isaac Newton's elusive 'n-body problem' and the prestigious prize offered to anyone with a solution, things begin to make sense. But with further deaths occurring and the threat of an innocent man being condemned, Vanessa must hurry with her calculations . . .

The Restricted Three-Body Problem and Holomorphic Curves

The Restricted Three-Body Problem and Holomorphic Curves PDF

Author: Urs Frauenfelder

Publisher: Springer

Published: 2018-08-29

Total Pages: 374

ISBN-13: 3319722786

DOWNLOAD EBOOK →

The book serves as an introduction to holomorphic curves in symplectic manifolds, focusing on the case of four-dimensional symplectizations and symplectic cobordisms, and their applications to celestial mechanics. The authors study the restricted three-body problem using recent techniques coming from the theory of pseudo-holomorphic curves. The book starts with an introduction to relevant topics in symplectic topology and Hamiltonian dynamics before introducing some well-known systems from celestial mechanics, such as the Kepler problem and the restricted three-body problem. After an overview of different regularizations of these systems, the book continues with a discussion of periodic orbits and global surfaces of section for these and more general systems. The second half of the book is primarily dedicated to developing the theory of holomorphic curves - specifically the theory of fast finite energy planes - to elucidate the proofs of the existence results for global surfaces of section stated earlier. The book closes with a chapter summarizing the results of some numerical experiments related to finding periodic orbits and global surfaces of sections in the restricted three-body problem. This book is also part of the Virtual Series on Symplectic Geometry http://www.springer.com/series/16019

Celestial Encounters

Celestial Encounters PDF

Author: Florin Diacu

Publisher: Princeton University Press

Published: 2020-12-08

Total Pages: 255

ISBN-13: 0691221839

DOWNLOAD EBOOK →

Celestial Encounters is for anyone who has ever wondered about the foundations of chaos. In 1888, the 34-year-old Henri Poincaré submitted a paper that was to change the course of science, but not before it underwent significant changes itself. "The Three-Body Problem and the Equations of Dynamics" won a prize sponsored by King Oscar II of Sweden and Norway and the journal Acta Mathematica, but after accepting the prize, Poincaré found a serious mistake in his work. While correcting it, he discovered the phenomenon of chaos. Starting with the story of Poincaré's work, Florin Diacu and Philip Holmes trace the history of attempts to solve the problems of celestial mechanics first posed in Isaac Newton's Principia in 1686. In describing how mathematical rigor was brought to bear on one of our oldest fascinations--the motions of the heavens--they introduce the people whose ideas led to the flourishing field now called nonlinear dynamics. In presenting the modern theory of dynamical systems, the models underlying much of modern science are described pictorially, using the geometrical language invented by Poincaré. More generally, the authors reflect on mathematical creativity and the roles that chance encounters, politics, and circumstance play in it.

The Three-Body Problem

The Three-Body Problem PDF

Author: C. Marchal

Publisher: Elsevier

Published: 2012-12-02

Total Pages: 593

ISBN-13: 0444600744

DOWNLOAD EBOOK →

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.

Lanterna Rally - Theme by Grace Themes