Regularization of the three body isosceles problem with a zero area-vector

Details Regularization of the three body isosceles problem with a zero area-vector Regularization of the three body isosceles problem with a zero area-vector

Apr 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977dossr.233.1049s&link_type=abstract

Akademiia Nauk SSSR, Doklady, vol. 233, Apr. 21, 1977, p. 1049-1052. In Russian.

Mathematics

Celestial Mechanics, Center Of Gravity, Hyperbolic Trajectories, Three Body Problem, Vectors (Mathematics), Asymptotic Methods, Canonical Forms, Collisions, Equations Of Motion, Hamiltonian Functions, Trajectory Analysis

Scientific paper

Canonical differential equations are presented for the final dynamics in a three body isosceles problem. These equations do not specify flux on an isoenergetic manifold since each trajectory of the canonical system leaves this manifold in a finite time span due to binary and ternary collisions. But through appropriate coordinate and time substitutions, it is possible to extend the isoenergetic manifold to a manifold with an edge, thus extending the flux to the edge. This procedure permits one to describe the asymptotic behavior of the solutions of the plane three body isosceles problem, the Sundman method (1912) used to regularize binary collisions.

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