Kinematic Orbits and the Structure of the Internal Space for Systems of Five or More Bodies

Details Kinematic Orbits and the Structure of the Internal Space for Systems of Five or More Bodies Kinematic Orbits and the Structure of the Internal Space for Systems of Five or More Bodies

1999-09-30

arxiv.org/abs/physics/9910001v1

Physics

Chemical Physics

38 pages, submitted to J. Phys. A

Scientific paper

10.1088/0305-4470/33/7/309

The internal space for a molecule, atom, or other n-body system can be conveniently parameterised by 3n-9 kinematic angles and three kinematic invariants. For a fixed set of kinematic invariants, the kinematic angles parameterise a subspace, called a kinematic orbit, of the n-body internal space. Building on an earlier analysis of the three- and four-body problems, we derive the form of these kinematic orbits (that is, their topology) for the general n-body problem. The case n=5 is studied in detail, along with the previously studied cases n=3,4.

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