Other
Scientific paper
Jun 1982
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982cemec..27..167k&link_type=abstract
Celestial Mechanics, vol. 27, June 1982, p. 167-178.
Other
Angular Momentum, Equipotentials, Many Body Problem, Parameterization, Particle Motion, Three Body Problem, Algorithms, Kinetic Energy, Particle Interactions, Root-Mean-Square Errors
Scientific paper
A new approach to the n-body problem in terms of an rms particle velocity and a harmonic mean particle separation has been constructed by using averaging procedures formulated in terms of a single parameter. A systematic classification of escape and collision processes by means of specific polynomials, which can be used somewhat like generating functions, is introduced. For n-body problems with non-null total angular momentum, an rms angular momentum is defined which together with a harmonic mean centroidal moment of inertia characterizes the rotational kinetic energy. Finally, a graphical construction for the equipotentials of the three-body problem is given and attention is drawn to the use of the apex, defined as the point of least average separation, in this problem. It is supposed that the n-bodies interact with one another via the Newtonian potential in an inertial system.
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