Mathematics
Scientific paper
Sep 1979
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979crasm.289..299i&link_type=abstract
Academie des Sciences (Paris), Comptes Rendus, Serie A - Sciences Mathematiques, vol. 289, no. 4, Sept. 17, 1979, p. 299-302. In
Mathematics
Celestial Mechanics, Collisions, Three Body Problem, Orbital Mechanics, Singularity (Mathematics)
Scientific paper
The planar three-body problem is stated according to the idea used by McGehee (1974) in the study of the rectilinear three-body problem, in order to examine the singularity associated with a triple collision. A transformation of variables is applied to the eighth-order system of differential equations governing the motion of the bodies in order to obtain a set of equations which are defined at the tripple-collision singularity, and it is noted that the triple collision takes place in this formulation if and only if the moment of inertia of the system is zero. The velocity variables in the energy integral are transformed as well, leading to a system of equations defining an invariant manifold for the triple collision. A second change of variables is then applied to the system of equations and integrals, resulting in the definition of two manifolds, integrable by quadratures to determine the moment of inertia.
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