Computer Science – Numerical Analysis
Scientific paper
Oct 1974
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1974cemec..10..217h&link_type=abstract
Celestial Mechanics, vol. 10, Oct. 1974, p. 217-241.
Computer Science
Numerical Analysis
41
Equations Of Motion, Gravitational Effects, Many Body Problem, Three Body Problem, Boundary Value Problems, Computer Programs, Hamiltonian Functions, Matrices (Mathematics), Numerical Analysis, Particle Collisions, Singularity (Mathematics), Transformations (Mathematics)
Scientific paper
The work of Aarseth and Zare (1974) is extended to provide a global regularization of the classical gravitational three-body problem. By transformation of the variables in a way that does not depend on the particular configuration, equations of motion are obtained which are regular with respect to collisions between any pair of particles. The only cases excepted are those in which collisions between more than one pair occur simultaneously and those in which at least one of the masses vanishes. However, by means of the same principles, the restricted problem is regularized globally if collisions between the two primaries are excluded. Results of numerical tests are summarized, and the theory is generalized to provide global regularizations, first, for perturbed three-body motion and, second, for the N-body problem.
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