arXiv subjects

Ethan Burnett

Publications and source records attributed to Ethan Burnett.

6 recordsLinked to original sources

arXiv2026

Analytic Non-Gaussian Confidence Boundary Method for Chance-Constrained Trajectory Control

Standard chance constrained control algorithms typically rely on the assumption that uncertainties in vehicle states obey Gaussian statistics. Highly nonlinear systems tend to disrupt Gaussianity, challenging standard chance-constrained control methods. This paper develops a non-Gaussian confidence boundary parameterization technique for such cases where the problem departs appreciably from the Gaussian assumption. The approach is to consider the true confidence boundary as a perturbation of the one predicted from covariance, deriving perturbed boundary geometry from computed higher-order statistical moments. Applying this technique to so-called "banana-shaped distributions" (found e.g. in orbital mechanics problems) enables a simple parameterization of the confidence boundary using the skew and kurtosis tensors. The method is then applied to an impulsive stochastic spacecraft maneuver targeting problem in two-body dynamics. An algorithmic implementation outperforms a standard linear covariance-based approach in computing control parameters satisfying certain probabilistic bounds on the non-Gaussian distribution.

math.OC↗

arXiv2023

Spin-Orbit Coupling of Europa's Ice Shell and Interior

Europa is an icy ocean world, differentiated into a floating ice shell and solid interior, separated by a global ocean. The classical spin-orbit coupling problem considers a satellite as a single rigid body, but in the case of Europa, the existence of the subsurface ocean enables independent motion of the ice shell and solid interior. This paper explores the spin-orbit coupling problem for Europa from a dynamical perspective, yielding illuminating analytical and numerical results. We determine that the spin behavior of Europa is influenced by processes not captured by the classical single rigid body spin-orbit coupling analysis. The tidal locking process for Europa is governed by the strength of gravity-gradient coupling between the ice shell and solid interior, with qualitatively different behavior depending on the scale of this effect. In this coupled rigid model, the shell can potentially undergo large angular displacements from the solid interior, and the coupling plays an outsize role in the dynamical evolution of the moon, even without incorporating the dissipative effects of shell non-rigidity. We additionally discuss the effects of a realistic viscoelastic shell, and catalogue other torques that we expect to be sub-dominant in Europa's spin dynamics, or whose importance is unknown. Finally, we explore how the choice of tidal model affects the resulting equilibrium spin state.

astro-ph.EP↗

arXiv2021

Spacecraft Relative Motion Dynamics and Control Using Fundamental Solution Constants

This paper explores expressing the relative state in the close-proximity satellite relative motion problem in terms of fundamental solution constants. The nominal uncontrolled relative state can be expressed in terms of a weighted sum of fundamental and geometrically insightful motions. These fundamental motions are obtained using Lyapunov-Floquet theory. In the case that the dynamics are perturbed by the action of a controller or by unmodeled dynamics, the weights on each fundamental solution are allowed to vary as in a variation-of-parameters approach, and in this manner function as state variables. This methodology reveals interesting insights about satellite relative motion and also enables elegant control approaches. This approach can be applied in any dynamical environment as long as the chief orbit is periodic, and this is demonstrated with results for relative motion analysis and control in the eccentric Keplerian problem and in the circular restricted three-body problem (CR3BP). Some commentary on extension of the methodology beyond the periodic chief orbit case is also provided. This is a promising and widely applicable new approach to the close-proximity satellite relative motion problem.

math.OC↗

arXiv2021

Approximating Orbits in a Rotating Gravity Field with Oblateness and Ellipticity Perturbations

This paper explores the problem of analytically approximating the orbital state for a subset of orbits in a rotating potential with oblateness and ellipticity perturbations. This is done by isolating approximate differential equations for the orbit radius and other elements. The conservation of the Jacobi integral is used to make the problem solvable to first-order in the perturbations. The solutions are characterized as small deviations from an unperturbed circular orbit. The approximations are developed for near-circular orbits with initial mean motion $n_{0}$ around a body with rotation rate $c$. The approximations are shown to be valid for values of angular rate ratio $Γ= c/n_{0} > 1$, with accuracy decreasing as $Γ\rightarrow 1$, and singularities at and near $Γ= 1$. Extensions of the methodology to eccentric orbits are discussed, with commentary on the challenges of obtaining generally valid solutions for both near-circular and eccentric orbits.

astro-ph.EP↗

arXiv2021

Geometric Perspectives on Fundamental Solutions in the Linearized Satellite Relative Motion Problem

Understanding natural relative motion trajectories is critical to enable fuel-efficient multi-satellite missions operating in complex environments. This paper studies the problem of computing and efficiently parameterizing satellite relative motion solutions for linearization about a closed chief orbit. By identifying the analytic relationship between Lyapunov-Floquet transformations of the relative motion dynamics in different coordinate systems, new means are provided for rapid computation and exploration of the types of close-proximity natural relative motion available in various applications. The approach is demonstrated for the Keplerian relative motion problem with general eccentricities in multiple coordinate representations. The Keplerian assumption enables an analytic approach, leads to new geometric insights, and allows for comparison to prior linearized relative motion solutions.

cs.RO↗

arXiv2021

Europa's Hemispheric Color Dichotomy as a Constraint on Non-synchronous Rotation

Europa's surface reflectance exhibits a pronounced hemispheric dichotomy, which is hypothesized to form due to enhanced irradiation of the trailing hemisphere by energetic particles entrained in the jovian magnetosphere. We propose that this pattern can only persist if the timescale for discoloration is much shorter than that of Europa's rotation relative to the synchronous state, and provide a means for constraining the rotation rate using the observed color pattern. By decomposing the longitudinal ultraviolet and visible color variations from Voyager data into sine and cosine terms, we find no detectable signature of non-synchronous rotation (NSR). This same conclusion is reached with two observational models of discoloration: one representing an actively discoloring surface, and the other assuming that the present-day exogenic discoloration on the surface is in steady-state. Magnitudes of the expected signature are presented as functions of the age of the crater Pwyll, which is used to constrain the timescale of discoloration. Furthermore, we develop a physical model of discoloration to validate the geometric models, producing consistent results. The failure to identify a signature of NSR using Europa's hemispheric color dichotomy magnifies the outstanding problem of the origin of the stress to explain Europa's pervasive tectonic features.

astro-ph.EP↗