Sufficient conditions for the absence of collisions in the three-body problem

Details Sufficient conditions for the absence of collisions in the three-body problem Sufficient conditions for the absence of collisions in the three-body problem

Apr 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977azh....54..425g&link_type=abstract

Astronomicheskii Zhurnal, vol. 54, Mar.-Apr. 1977, p. 425-428. In Russian.

Mathematics

Celestial Mechanics, Three Body Problem, Collisions, Equations Of Motion, Existence Theorems, Hamiltonian Functions, Matrices (Mathematics)

Scientific paper

A theorem concerning collisionless motion is presented and proven for the three-body problem in which the motion of the two smaller bodies is described by a Hamiltonian system. This theorem is used to obtain sufficient conditions for initial data under which three-body motion occurs without binary or triple collisions. The example of the sun and two planets is employed in the analysis.

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