arXiv subjects

Kathleen C. Howell

Publications and source records attributed to Kathleen C. Howell.

9 recordsLinked to original sources

arXiv2026

Elliptical Lunar Frozen Orbit Constellations: Torus-Based Design and Analysis

Elliptical Lunar Frozen Orbits (ELFOs) are attractive candidates for lunar satellite constellations supporting lunar south pole exploration. Building on prior frequency-based orbit analysis methods, this investigation develops a torus-based, frequency-domain framework for constellation-level ELFO design and analysis. Within a doubly-averaged dynamical model, each ELFO is characterized by three frequency-angle pairs; a systematic comparison across progressively higher-fidelity models identifies the additional frequency components introduced at each level. The angular parametrization admits multiple symmetries that substantially reduce the design space, enabling a rapid, epoch-free global survey of constellation configurations. A higher-fidelity refinement and analysis layer then combines a (1) Frequency-Domain Differential Corrector (FDDC) that targets desired frequency properties and suppresses undesired long-period oscillations, (2) Fourier surrogate re-optimization for inter-satellite phasing without propagation in the loop, and (3) spectral attribution that separates design-refinable coverage losses from those inherent to the dynamics. Together, these elements supply a fidelity-bridging and diagnostic framework for ELFO constellation design and analysis.

math.DS↗

arXiv2026

Families of Two-Impulse Optimal Rendezvous Transfers Between Elliptic Orbits

The classical fuel-optimal two-impulse rendezvous problem between Keplerian orbits is revisited from a family-based perspective. Conventional approaches often yield isolated optimal solutions whose mutual relationships remain unclear; yet, when re-parameterized appropriately, seemingly unrelated optima are revealed to be connected members of continuous solution families. To expose this structure, the proposed framework enforces a subset of first-order necessary optimality conditions and traces the resulting one-parameter families via numerical continuation. The families are classified using Hessian-based criteria and Primer Vector Theory, and are projected onto porkchop plots to connect the angular and temporal domains. Representative case studies reveal the emergence, merging, and disappearance of locally optimal branches under variations in orbital geometry, supplying a global map of the solution landscape. This complementary perspective clarifies the robustness of optimal solutions and identifies alternative near-optimal transfers in the vicinity of a nominal trajectory.

math.OC↗

arXiv2026

Linking Averaged and Unaveraged Three-Body Dynamics Near Smaller Primaries: Symmetric Periodic Orbits

Within a three-body system comprised of two celestial bodies and a spacecraft, the dynamical environment near a smaller primary is significantly perturbed, motivating a balance between global insight and model fidelity. While averaged dynamics offer an integrable model to classify solution landscapes, they inherently lack the accuracy of the unaveraged dynamics, such as the Hill Restricted Three-Body Problem and Circular Restricted Three-Body Problem. This work establishes a systematic bridge between the averaged and unaveraged regimes by explicitly linking averaged equilibria to symmetric periodic orbits in the unaveraged three-body systems. A unified frequency framework is introduced to characterize the mapping of invariant tori across the dynamical models. Leveraging the parity of the resonance ratio, an initialization scheme is developed to identify admissible apse configurations, enabling the a priori prediction of solution multiplicity and symmetry types. Furthermore, the global evolution of families derived from averaged equilibria is traced via bifurcation and frequency analysis. These findings are synthesized into archetypical bifurcation diagrams, providing a comprehensive atlas of the symmetric periodic orbit web within the HR3BP and CR3BP. The resulting framework not only clarifies the topological origins of complex periodic orbit families but also offers a versatile tool for trajectory design in cislunar and multi-body environments.

math.DS↗

arXiv2025

On-Manifold Low-Thrust Rephasing of Quasi-Periodic Orbits

A bi-level optimal control framework is introduced to solve the low-thrust re-phasing problem on quasi-periodic invariant tori in multi-body environments where deviations away from the torus during maneuver are considered unsafe or irresponsible. It is shown for a large class of mechanical systems that conformity to the torus manifold during periods of non-zero control input is infeasible. The most feasible trajectories on the torus surface are generated through the minimization of fictitious control input in the torus space using phase space control variables mapped via the torus function. These reference trajectories are then transitioned to the phase space both through a minimum tracking error homotopy and minimum time patched solutions. Results are compared to torus agnostic low-thrust transfers using measures of fuel consumption, cumulative torus error, and coast time spent on the torus during maneuver. Modifications to the framework are made for the inclusion of quasi-periodically forced dynamical systems. Lastly, minimum time recovery trajectories with free final torus conditions expose the disparity between the proposed framework and torus agnostic approaches. Examples are drawn from the circular and elliptical restricted three-body problems.

nlin.CD↗

arXiv2025

A Frequency-Domain Differential Corrector for Quasi-Periodic Trajectory Design and Analysis

This paper introduces the Frequency-Domain Differential Corrector (FDDC), a model-agnostic approach for constructing quasi-periodic orbits (QPOs) across a range of dynamical regimes. In contrast to existing methods that explicitly enforce an invariance condition in all frequency dimensions, the FDDC targets dominant spectral components identified through frequency-domain analysis. Leveraging frequency refinement strategies such as Laskar-Numerical Analysis of Fundamental Frequency (L-NAFF) and Gómez-Mondelo-Simó-Collocation (GMS-C), the method enables efficient and scalable generation of high-dimensional QPOs. The FDDC is demonstrated in both single- and multiple-shooting formulations. While the study focuses on the Earth-Moon system, the framework is broadly applicable to other celestial environments. Sample applications include Distant Retrograde Orbits (DROs), Elliptical Lunar Frozen Orbits (ELFOs), and Near Rectilinear Halo Orbits (NRHOs), illustrating constellation design and the recovery of analog solutions in higher-fidelity models. With its model-independent formulation and spectral targeting capabilities, FDDC offers a versatile tool for robust trajectory design and mission planning in complex dynamical systems.

math.DS↗

arXiv2024

Direct low-energy trajectories to Near-Earth Objects

Near-Earth Objects (NEOs) are asteroids, comets and meteoroids in heliocentric orbits with perihelion below 1.3 au. Similarly to the population of the Main Asteroid Belt, NEOs are primordial bodies and their study can improve our understanding of the origins of the Solar System. With a catalog of over 30~000 known asteroids and approximately 100 listed short-period comets, the NEO population represents an inventory of exploration targets reachable with significantly lower cost than the objects of the Main Asteroid Belt. In addition, the materials present in these bodies could be used to resupply spacecraft en route to other destinations. The trajectories of past missions to NEOs have been designed with the patched-conics technique supplemented by impulsive and/or low-thrust maneuvers and planetary gravity assist. The transfer times range from some months to a few years, and the close-approach speeds relative to the target have been as high as 10 km/s. The design technique described in this work leverages the invariant structures of the circular restricted three-body problem (CR3BP) to connect the vicinity of the Earth with NEOs in low-eccentricity, low-inclination orbits. The fundamental building blocks are periodic orbits around the collinear points L$_1$ and L$_2$ of the Sun-Earth CR3BP. These orbits are used to generate paths that follow the associated hyperbolic invariant manifolds, exit the sphere of influence of the Earth and reach NEOs on nearby orbits. The strategy is simple, can be applied to depart either a libration point orbit or the vicinity of the Earth, and offers attractive performance features.

astro-ph.EP↗

arXiv2023

Transfers between moons with escape and capture patterns via Lyapunov exponent maps

This contribution focuses on the design of low-energy transfers between planetary moons and presents an efficient technique to compute trajectories characterized by desirable behaviors in the vicinities of the departure and destination bodies. The method utilizes finite-time Lyapunov exponent maps in combination with the Moon-to-Moon Analytical Transfer (MMAT) method previously proposed by the authors. The integration of these two components facilitates the design of direct transfers between moons within the context of the circular restricted three-body problem, and allows the inclusion of a variety of trajectory patterns, such as captures, landings, transits and takeoffs, at the two ends of a transfer. The foundations and properties of the technique are illustrated through an application based on impulsive direct transfers between Ganymede and Europa. However, the methodology can be employed to assist in the design of more complex mission scenarios, such as moon tours.

nlin.CD↗

arXiv2021

Transfer design between neighborhoods of planetary moons in the circular restricted three-body problem

Given the interest in future space missions devoted to the exploration of key moons in the solar system and that may involve libration point orbits, an efficient design strategy for transfers between moons is introduced that leverages the dynamics in these multi-body systems. The moon-to-moon analytical transfer (MMAT) method is introduced, comprised of a general methodology for transfer design between the vicinities of the moons in any given system within the context of the circular restricted three-body problem, useful regardless of the orbital planes in which the moons reside. A simplified model enables analytical constraints to efficiently determine the feasibility of a transfer between two different moons moving in the vicinity of a common planet. In particular, connections between the periodic orbits of such two different moons are achieved. The strategy is applicable for any type of direct transfers that satisfy the analytical constraints. Case studies are presented for the Jovian and Uranian systems. The transition of the transfers into higher-fidelity ephemeris models confirms the validity of the MMAT method as a fast tool to provide possible transfer options between two consecutive moons.

astro-ph.EP↗

arXiv2020

Extraction and Visualization of Poincaré Map Topology for Spacecraft Trajectory Design

Mission designers must study many dynamical models to plan a low-cost spacecraft trajectory that satisfies mission constraints. They routinely use Poincaré maps to search for a suitable path through the interconnected web of periodic orbits and invariant manifolds found in multi-body gravitational systems. This paper is concerned with the extraction and interactive visual exploration of this structural landscape to assist spacecraft trajectory planning. We propose algorithmic solutions that address the specific challenges posed by the characterization of the topology in astrodynamics problems and allow for an effective visual analysis of the resulting information. This visualization framework is applied to the circular restricted three-body problem (CR3BP), where it reveals novel periodic orbits with their relevant invariant manifolds in a suitable format for interactive transfer selection. Representative design problems illustrate how spacecraft path planners can leverage our topology visualization to fully exploit the natural dynamics pathways for energy-efficient trajectory designs.

nlin.CD↗