A new regularization of the restricted three-body problem and an application

Details A new regularization of the restricted three-body problem and an application A new regularization of the restricted three-body problem and an application

Dec 1981

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981cemec..25..397b&link_type=abstract

Celestial Mechanics, vol. 25, Dec. 1981, p. 397-415.

Mathematics

4

Equations Of Motion, Orbital Mechanics, Three Body Problem, Transformations (Mathematics), Collisions, Coordinates, Matrices (Mathematics)

Scientific paper

A new regularizing transformation is constructed for the three-dimensional restricted three-body problem. The transformation is derived explicitly and is equivalent to a simple rational map; it is also geometrically equivalent to the rotation of the three-sphere. The regularizing map is compared to the KS map, a generalization of the two dimensional Levi-Civita map. Unlike the KS map, it is both dimension preserving and valid in n dimensions. The regularizing map is applied to the restricted problem in order to prove the existence of a family of periodic orbits which continue from a family of collision orbits.

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