Author : Christopher Keil McCord
Publisher : American Mathematical Soc.
ISBN 13 : 0821806920
Total Pages : 91 pages
Book Rating : 4.8/5 (218 download)
Book Synopsis The Integral Manifolds of the Three Body Problem by : Christopher Keil McCord
Download or read book The Integral Manifolds of the Three Body Problem written by Christopher Keil McCord and published by American Mathematical Soc.. This book was released on 1998 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt: The phase space of the spatial three-body problem is an open subset in ${\mathbb R}^{18}$. Holding the ten classical integrals of energy, center of mass, linear and angular momentum fixed defines an eight dimensional submanifold. 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 Birkhoff's conjecture that the bifurcations occur only at central configurations.