Connecting the Equinoctial Elements and Rodrigues Parameters: A New Set of Elements

TL;DR

This paper introduces a new set of equinoctial elements linked to Rodrigues parameters, eliminating singularities and improving trajectory optimization for retrograde equatorial orbits.

Contribution

It develops a novel set of equinoctial elements based on modified Rodrigues parameters, enhancing orbital analysis and optimization methods.

Findings

The new elements remove coordinate singularities for retrograde equatorial orbits.

Numerical experiments show improved convergence in trajectory optimization.

The geometric interpretation links equinoctial elements with attitude dynamics.

Abstract

A geometric interpretation of the equinoctial elements is given with a connection to orthogonal rotations and attitude dynamics in Euclidean 3-space. An identification is made between the equinoctial elements and classic Rodrigues parameters. A new set of equinoctial elements are developed using the modified Rodrigues parameters, thereby removing the coordinate singularity for retrograde equatorial orbits present in previous versions of these elements. A low-thrust trajectory optimization problem is set up using the new elements to numerically verify convergence for the two-point boundary problem, as compared to their predecessors.