Motion near quadruple collision in the trapezoidal four-body problem

Details Motion near quadruple collision in the trapezoidal four-body problem Motion near quadruple collision in the trapezoidal four-body problem

Sep 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983cemec..31...23l&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 31, Sept. 1983, p. 23-41. In French.

Mathematics

Collisions, Many Body Problem, Trapezoids, Celestial Mechanics, Manifolds (Mathematics), Topology

Scientific paper

The trapezoidal four-body problem is investigated, focusing on the dimensions and interconnections of the invariant subvarieties of the hyperbolic equilibrium points in this quadruple collision problem. The existence of certain solutions for the problem in the vicinity of the quadruple collisions is shown. For certain values of the mass ratio parameter, there exist bifurcations which are accounted for by the joining (or not) of the orbits between diverse regions at rest. Several simplifications are employed for the four-body problem, in particular, the symmetries, the nonexistence of triple collisions, and the combining of two simpler problems with one less degree of freedom. The degree of difficulty of this problem is about the same as the general plane three-body problem when the angular momentum is zero.

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