Regularization of restricted 3-body problems. (English) Zbl 1351.70012

Summary: Using geometric mechanics we regularize the binary collisions of planar restricted three-body problems (with zero and nonzero angular momentum). The regularization is general enough to allow the primaries to move under any arbitrary dynamics and has as special cases all the classical restricted three-body problems, namely; circular, elliptic, parabolic and hyperbolic. This generalizes the classical procedures of T. Levi-Civita [Acta Math. 42, 99–144 (1920; JFM 47.0837.01)], G. D. Birkhoff [Ann. Sc. Norm. Super. Pisa, II. Ser. 4, 267–306 (1935; Zbl 0012.12804, JFM 61.1480.03)], T. N. Thiele [Astron. Nachr. 138, 1–10 (1895; JFM 26.1098.01)] and C. Burrau [Vierteljahrsschr. Astron. Ges. 41, 261–266 (1906; JFM 37.0968.01)]. Explicit formulas are given for the regularizations.


70F07 Three-body problems
70F15 Celestial mechanics
70H15 Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics
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