Integration of the equations of planetary motion in rectangular coordinates

Abstract

Matrix methods for the approximate solution of differential equations are applied to the development of general perturbations in rectangular coordinates. The solution is obtained directly in the form of comple- mentary function and particular integral. The possible role of the arbitrary constants is discussed; these appear unambiguously in the complementary function, the nature of which is known from the properties of Keplerian motion. Formulas for the application of this method to the calculation of special perturbations are also included.