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The Integral Manifolds of the Three Body Problem
Christopher Keil McCordKenneth Ray MeyerQuidong Wang
出版American Mathematical Soc., 1998
主題Mathematics / AppliedMathematics / Geometry / GeneralMathematics / Geometry / DifferentialScience / Space Science / AstronomyScience / Mechanics / GeneralScience / Physics / General
ISBN08218069209780821806920
URLhttp://books.google.com.hk/books?id=ao_TCQAAQBAJ&hl=&source=gbs_api
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註釋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.