A generalization of the equinoctial orbital elements

We introduce six quantities that generalize the equinoctial orbital elements when some or all the perturbing forces that act on the propagated body are derived from a potential. Three of the elements define a non-osculating ellipse on the orbital plane, other two fix the orientation of the equinoctial reference frame, and the last allows us to determine the true longitude of the body. The Jacobian matrices of the transformations between the new elements and the position and velocity are explicitly given. As a possible application, we investigate their use in the propagation of Earth’s artificial satellites, showing a remarkable improvement compared to the equinoctial orbital elements.