TABLE OF CONTENTS The mathematical theory of orbital mechanics in terms of the nonsingular equinoctial orbit elements has benefited from the contribution of Broucke and Cefola in Ref. [2], who took advantage of the well-established results concerning the Lagrange and Poisson brackets of classical elements that are found, for example, in Refs. [3] and [4] in order to transform these brackets in terms of the nonsingular elements. Cefola later developed the single-averaged variation of parameters equations for these elements in Ref. [5], which were applied by Edelbaum, Sackett, and Malchow in Ref. [6] to the problem of optimal low-thrust transfer. Further applications of nonsingular orbit prediction and orbit-transfer optimization problems appeared in Refs. [7] and [8]. The variation of parameters perturbation equations based on the nonsingular equinoctial orbit elements are free from singularities for zero eccentricity and 0- and 90-deg inclination orbits. This fact, as well as many additional properties of the equinoctial elements, are derived in a systematic way in Ref. [2]. The matrizant, or state transition matrix corresponding to these elements, is based on the partial derivatives of the position and velocity vectors with respect to the equinoctial elements as well as the inverse partial derivatives, meaning the partial derivatives of the equinoctial elements with respect to the position and velocity vectors. These partials were derived in Ref. [2] in terms of the classical elements, and transformed later in Refs. [5]
