The Integral Manifolds of the Three Body Problem

The Integral Manifolds of the Three Body Problem
Author: Christopher Keil McCord
Publisher: American Mathematical Soc.
Total Pages: 106
Release: 1998
Genre: Mathematics
ISBN: 0821806920

The phase space of the spatial three-body problem is an open subset in R18. Holding the ten classical integrals of energu, center of mass, linear and angular momentum fixed defines an eight dimensional manifold. For fixed nonzero angular momentum, the topology of this manifold depends only on the energy. This volume computes the homology of this manifold for all energy values. This table of homology shows that for negative energy, the integral manifolds undergo seven bifurcations. Four of these are the well-known bifurcations due to central configurations, and three are due to "critical points at infinity". This disproves Birkhoffs conjecture that the bifurcations occur only at central configurations.

Hamiltonian Systems And Celestial Mechanics (Hamsys-98) - Proceedings Of The Iii International Symposium

Hamiltonian Systems And Celestial Mechanics (Hamsys-98) - Proceedings Of The Iii International Symposium
Author: J Delgado
Publisher: World Scientific
Total Pages: 373
Release: 2000-10-09
Genre: Science
ISBN: 9814492116

This volume is an outgrowth of the Third International Symposium on Hamiltonian Systems and Celestial Mechanics. The main topics are Arnold diffusion, central configurations, singularities in few-body problems, billiards, area-preserving maps, and geometrical mechanics. All papers in the volume went through the refereeing process typical of a mathematical research journal.

New Advances in Celestial Mechanics and Hamiltonian Systems

New Advances in Celestial Mechanics and Hamiltonian Systems
Author: JoaquĆ­n Delgado
Publisher: Springer Science & Business Media
Total Pages: 261
Release: 2012-12-06
Genre: Mathematics
ISBN: 1441990585

The aim of the IV International Symposium on Hamiltonian Systems and Celestial Mechanics, HAMSYS-2001 was to join top researchers in the area of Celestial Mechanics, Hamiltonian systems and related topics in order to communicate new results and look forward for join research projects. For PhD students, this meeting offered also the opportunity of personal contact to help themselves in their own research, to call as well and promote the attention of young researchers and graduated students from our scientific community to the above topics, which are nowadays of interest and relevance in Celestial Mechanics and Hamiltonian dynamics. A glance to the achievements in the area in the last century came as a consequence of joint discussions in the workshop sessions, new problems were presented and lines of future research were delineated. Specific discussion topics included: New periodic orbits and choreographies in the n-body problem, singularities in few body problems, central configurations, restricted three body problem, geometrical mechanics, dynamics of charged problems, area preserving maps and Arnold diffusion.

Equadiff 99 (In 2 Volumes) - Proceedings Of The International Conference On Differential Equations

Equadiff 99 (In 2 Volumes) - Proceedings Of The International Conference On Differential Equations
Author: Bernold Fiedler
Publisher: World Scientific
Total Pages: 838
Release: 2000-09-05
Genre: Mathematics
ISBN: 9814522163

This book is a compilation of high quality papers focussing on five major areas of active development in the wide field of differential equations: dynamical systems, infinite dimensions, global attractors and stability, computational aspects, and applications. It is a valuable reference for researchers in diverse disciplines, ranging from mathematics through physics, engineering, chemistry, nonlinear science to the life sciences.

International Conference on Differential Equations, Berlin, Germany, 1-7 August, 1999

International Conference on Differential Equations, Berlin, Germany, 1-7 August, 1999
Author: Bernold Fiedler
Publisher: World Scientific
Total Pages: 846
Release: 2000
Genre: Differential equations
ISBN: 9789810249885

This book is a compilation of high quality papers focussing on five major areas of active development in the wide field of differential equations: dynamical systems, infinite dimensions, global attractors and stability, computational aspects, and applications. It is a valuable reference for researchers in diverse disciplines, ranging from mathematics through physics, engineering, chemistry, nonlinear science to the life sciences

Celestial Mechanics

Celestial Mechanics
Author: Donald Saari
Publisher: American Mathematical Soc.
Total Pages: 282
Release: 2002
Genre: Science
ISBN: 0821829025

This volume reflects the proceedings from an international conference on celestial mechanics held at Northwestern University (Evanston, IL) in celebration of Donald Saari's sixtieth birthday. Many leading experts and researchers presented their recent results. Don Saari's significant contribution to the field came in the late 1960s through a series of important works. His work revived the singularity theory in the $n$-body problem which was started by Poincare and Painleve. Saari'ssolution of the Littlewood conjecture, his work on singularities, collision and noncollision, on central configurations, his decompositions of configurational velocities, etc., are still much studied today and were reflected throughout the conference. This volume covers various topics of currentresearch, from central configurations to stability of periodic orbits, from variational methods to diffusion mechanisms, from the dynamics of secular systems to global dynamics of the solar systems via frequency analysis, from Hill's problem to the low energy transfer orbits and mission design in space travel, and more. This classic field of study is very much alive today and this volume offers a comprehensive representation of the latest research results.

The Collected Papers of Stephen Smale

The Collected Papers of Stephen Smale
Author: Stephen Smale
Publisher: World Scientific
Total Pages: 564
Release: 2000
Genre: Mathematics
ISBN: 9789810249922

This invaluable book contains the collected papers of Stephen Smale. These are divided into eight groups: topology; calculus of variations; dynamics; mechanics; economics; biology, electric circuits and mathematical programming; theory of computation; miscellaneous. In addition, each group contains one or two articles by world leaders on its subject which comment on the influence of Smale's work, and another article by Smale with his own retrospective views.

Hamiltonian Systems and Celestial Mechanics

Hamiltonian Systems and Celestial Mechanics
Author:
Publisher: World Scientific
Total Pages: 380
Release: 2000
Genre: Mathematics
ISBN: 9789810244637

This volume is an outgrowth of the Third International Symposium on Hamiltonian Systems and Celestial Mechanics. The main topics are Arnold diffusion, central configurations, singularities in few-body problems, billiards, area-preserving maps, and geometrical mechanics. All papers in the volume went through the refereeing process typical of a mathematical research journal.