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arXiv · 2505.12812

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

Joseph T. A. Peterson·Vishala Arya·John L. Junkins
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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.

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Joseph T. A. Peterson, Vishala Arya, John L. Junkins. 2025-05-19. Connecting the Equinoctial Elements and Rodrigues Parameters: A New Set of Elements. https://doi.org/10.2514/1.g007347

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