From Rotations and Inclinations to Zero Configurational Velocity Surfaces  Part One  a Natural Rotating Coordinate System
Abstract
Attempts are made to: (1) derive conditions which will lead to the clearest possible 'zero velocity' surfaces for the solutions of both the threebody and nbody problems; (2) determine the natural rotating coordinate system of an nbody 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 nbody problem solutions. Orbit inclination is used to illustrate the effects of this rotation.
 Publication:

Celestial Mechanics
 Pub Date:
 August 1984
 DOI:
 10.1007/BF01241046
 Bibcode:
 1984CeMec..33..299S
 Keywords:

 Cartesian Coordinates;
 Many Body Problem;
 Orbital Mechanics;
 Orbital Velocity;
 Rotating Bodies;
 Three Body Problem;
 Angular Velocity;
 Branching (Mathematics);
 Inclination;
 Inequalities;
 Jacobi Integral;
 Rigid Structures;
 Astronomy