Relation between various formulations of perturbation equations of celestial mechanics

Abstract

Orbital motion of a body can be found from Newtonian equation of motion. However, it is useful to express the motion through time derivatives of Keplerian orbital elements, mainly if the motion is perturbed by small perturbing force. The first set of equations for the time derivatives of the orbital elements can be derived from the equation of motion using Lagrange brackets. The second one by using equation of motion and perturbation acceleration decomposed to radial, transversal and normal components. This paper shows that the second type of the perturbation equations can be derived from the first type using simple mathematical operations.