State and Uncertainty Propagation Using Generalized Equinoctial Orbital Elements
Abstract
This thesis investigates a recently introduced orbital parameterization called the generalized equinoctial orbital elements that are defined with respect to the orbital system’s total energy, as opposed to the traditional equinoctial elements that are defined by only the kinetic energy of the orbiting object and potential energy from a point-mass central body. The total energy may include any potential energy arising from perturbing forces; thus, perturbed behaviors may be embedded within the elements. Equations of motion may be numerically integrated with a marked improvement in the typical tradeoff between accuracy and computational cost.
Generalized equinoctial elements have linearized uncertainty propagation equations which allow a Gaussian approximation to be preserved through time in the perturbed case. Propagation schemes for cislunar and J2 environments for both state and uncertainty are formulated in this thesis, and their performance is evaluated in the context of traditional state-of-the art state and uncertainty propagation schemes.
Testing demonstrates reduced error at larger step sizes and longer uncertainty realism preservation when embedding J2 perturbations in the generalized equinoctial elements. Lunar third body perturbations are better considered as separately from the embedded potential as an external force.
Subject
Orbital ElementsOrbit Propagation
Uncertainty Realism
Equinoctial Elements
Perturbed Orbits
Collections
Citation
McGee, Kyle W. (2023). State and Uncertainty Propagation Using Generalized Equinoctial Orbital Elements. Master's thesis, Texas A&M University. Available electronically from https : / /hdl .handle .net /1969 .1 /202822.