Zero velocity hypersurfaces for the general planar four body problem

Details Zero velocity hypersurfaces for the general planar four body problem Zero velocity hypersurfaces for the general planar four body problem

Aug 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985a%26a...149..462l&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 149, no. 2, Aug. 1985, p. 462-464.

Astronomy and Astrophysics

Astrophysics

5

Celestial Mechanics, Equations Of Motion, Four Body Problem, Angular Momentum, Jacobi Matrix Method, Kinetic Energy

Scientific paper

The angular momentum and the energy integral of the planar four-body problem are used to establish the equation of hypersurfaces which define regions of space where motion is allowed to take place. As in the case of the three-body problem (Bozis, 1976), that hypersurface exists for both negative and positive values of the energy of the system, but singularities in the equation, corresponding to all possible collisions between the bodies, always allow for at least two of the four bodies to escape. The generalization from three to four bodies suggests that this can probably be done for any number of bodies (greater than four).

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