Physics
Scientific paper
Oct 1976
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976crasb.283..245i&link_type=abstract
Academie des Sciences (Paris), Comptes Rendus, Serie B - Sciences Physiques, vol. 283, no. 8, Oct. 11, 1976, p. 245-248. In Fren
Physics
Celestial Mechanics, Collisions, Three Body Problem, Degrees Of Freedom, Dynamic Characteristics, Eigenvalues, Eigenvectors, Variational Principles
Scientific paper
The method used by Waldvogel (1976) for solving the equilateral three-body problem with triple collision is applied in the neighborhood of the rectilinear solutions with triple collision. Based on the rectilinear Lagrange solution that leads to a triple collision for t equals 0, neighboring solutions are sought with the aid of corresponding variational equations. Solution of these variational equations involves four characteristic exponents grouped in pairs and which depend on the mass ratios. A priori knowledge of one of these characteristic exponents enables the rest to be determined explicitly, and hence the first terms of the expansion of the general rectilinear solution near a triple-collision solution can be written, which depend on certain small arbitrary parameters, one of which is proportional to the generalized energy of the system.
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