Mathematics
Scientific paper
Aug 1984
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984cemec..33..299s&link_type=abstract
Celestial Mechanics (ISSN 0008-8714), vol. 33, Aug. 1984, p. 299-318.
Mathematics
15
Cartesian Coordinates, Many Body Problem, Orbital Mechanics, Orbital Velocity, Rotating Bodies, Three Body Problem, Angular Velocity, Branching (Mathematics), Inclination, Inequalities, Jacobi Integral, Rigid Structures
Scientific paper
Attempts are made to: (1) derive conditions which will lead to the clearest possible 'zero velocity' surfaces for the solutions of both the three-body and n-body problems; (2) determine the natural rotating coordinate system of an n-body system; and (3) derive an equation which will yield, as a special case, the Sundman inequality. The intimate connection among these aims is noted in the derivation of an intrinsic representation for the rigid body rotation of n-body problem solutions. Orbit inclination is used to illustrate the effects of this rotation.
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