Connecting the Equinoctial Elements and Rodrigues Parameters: A New Set of Elements
Systems and Control
2025-10-14 v2 Systems and Control
Dynamical Systems
Optimization and Control
Classical Physics
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.
Keywords
Cite
@article{arxiv.2505.12812,
title = {Connecting the Equinoctial Elements and Rodrigues Parameters: A New Set of Elements},
author = {Joseph T. A. Peterson and Vishala Arya and John L. Junkins},
journal= {arXiv preprint arXiv:2505.12812},
year = {2025}
}
Comments
formatting corrected for better readability