The Osculating H-Frame: A New Analytical Technique in Orbital Dynamics

摘要

The three-degree-of-freedom (point mass) equations of motion for a space vehicle with respect to a gravitating mass are derived first in terms of the H-Frame. The derivation is effected by using the expression for the velocity of the vehicle in planet-centered or heliocentric 'inertial' Cartesian coordinates (in this connotation the system is fixed in space and non-rotating) and the velocity determined in terms of spherical coordinates. Utilizing Lagrange's variation of parameters method, the rates of change of the H-Frame-referenced orbital elements are determined as functions of the perturbation forces (forces other than central gravitational). The technique is then applied to three specific problems wherein the intrinsic advantages become more apparent-- the motion of a vehicle in earth orbit, a cislunar trajectory, and the low-thrust powered flight of an interplanetary spacecraft.