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Regularization in the restricted four body problem. (English. Spanish summary) Zbl 1378.70011

Aguilar, M. (ed.) et al., Memorias de la Sociedad Matemática Mexicana. México: Sociedad Matemática Mexicana; México: Instituto de Matemáticas, UNAM. Aportaciones Matemáticas. Comunicaciones 45, 3-15 (2012).
Summary: The restricted (equilateral) four-body problem consists of three bodies of masses \(m_1\), \(m_2\) and \(m_3\) (called primaries) lying in a Lagrangian configuration of the three-body problem, i.e. they remain fixed at the apices of an equilateral triangle in a rotating coordinate system. A massless fourth body moves under the Newtonian gravitation law due to the three primaries; as in the restricted three-body problem the fourth mass does not affect the motion of the three primaries. In this paper we show a global regularization of binary collisions of the infinitesimal body with two of the primaries.
For the entire collection see [Zbl 1290.00026].

MSC:

70F16 Collisions in celestial mechanics, regularization
70F10 \(n\)-body problems
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