Abstract
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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Department of Aerospace Engineering and Engineering Mechanics.
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Waldvogel, J. A new regularization of the planar problem of three bodies. Celestial Mechanics 6, 221–231 (1972). https://doi.org/10.1007/BF01227784
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DOI: https://doi.org/10.1007/BF01227784