A practical and regular formulation of the N-body equations

Mathematics

Scientific paper

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Celestial Mechanics, Equations Of Motion, Hamiltonian Functions, Many Body Problem, Two Body Problem, Time Functions, Transformations (Mathematics)

Scientific paper

The method of Heggie (1974) is used to derive the globally regular equations of motion for the gravitational N-body problem, employing a modified notation to render the regularized Hamiltonian more tractable. Attention is also given to alternative time transformations and some differences in formulation. The use of a modified time transformation makes possible the treatment of two simultaneous pair collisions. The method is recommended for the study of small systems, especially when it is used only temporarily, for the integration of the system over critical interactions.

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