From Rotations and Inclinations to Zero Configurational Velocity Surfaces - Part One - a Natural Rotating Coordinate System

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.