A New Regularization of the Planar Problem of Three Bodies

Details A New Regularization of the Planar Problem of Three Bodies A New Regularization of the Planar Problem of Three Bodies

Sep 1972

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1972cemec...6..221w&link_type=abstract

Celestial Mechanics, Volume 6, Issue 2, pp.221-231

Physics

14

Scientific paper

A new method of simultaneously regularizing the three types of binary collisions in the planar problem of three bodies is developed: The coordinates are transformed by means of certain fourth degree polynomials, and a new independent variable is introduced, too. The proposed transformation is in each binary collision locally equivalent to Levi-Civita's transformation, whereas the singularity corresponding to a triple collision is mapped into infinity. The transformed Hamiltonian is a polynomial of degree 12 in the regularized variables.

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