David Arnas
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View article: Constructing Linear Operators Using Classical Perturbation Theory
Constructing Linear Operators Using Classical Perturbation Theory Open
This work introduces a methodology for generating linear operators that approximately represent nonlinear systems of perturbed ordinary differential equations. This is done through the application of classical perturbation theory via the L…
View article: Reliable and Repeatable Transit Through Cislunar Space Using the 2:1 Resonant Spatial Orbit Family
Reliable and Repeatable Transit Through Cislunar Space Using the 2:1 Resonant Spatial Orbit Family Open
This work focuses on the identification of reliable and repeatable spatial (three-dimensional) trajectories that link the Earth and the Moon. For this purpose, this paper aims to extend the 2:1 resonant prograde family and 2:1 resonant ret…
View article: Analytic frozen orbits under the zonal harmonics perturbation from an Earth-like planet
Analytic frozen orbits under the zonal harmonics perturbation from an Earth-like planet Open
This work focuses on providing closed form analytical expressions to define frozen orbits under the effects of the zonal harmonics of an Earth-like planet. Particularly, the perturbation effects from the terms J2, J3, J4, J5, J6, and J7 ar…
View article: Analytic frozen and other low eccentric orbits under J2 perturbation
Analytic frozen and other low eccentric orbits under J2 perturbation Open
This work presents an analytical perturbation method to define and study the dynamics of frozen orbits under the perturbation effects produced by the oblatness of the main celestial body. This is done using a perturbation method purely bas…
View article: Analytic transformation from osculating to mean elements under J2 perturbation
Analytic transformation from osculating to mean elements under J2 perturbation Open
This work presents an analytical perturbation method to study the dynamics of an orbiting object subject to the term $J_2$ from the gravitational potential of the main celestial body. This is done using a power series expansion in the pert…
View article: A Method for Generating Closely Packed Orbital Shells and the Implication on Orbital Capacity
A Method for Generating Closely Packed Orbital Shells and the Implication on Orbital Capacity Open
Shell-wise orbital slotting in Low Earth Orbit (LEO) can improve space safety, simplify space traffic coordination and management, and optimize orbital capacity. This paper describes two methods to generate 2D Lattice Flower Constellations…
View article: A Koopman Operator Tutorial with Othogonal Polynomials
A Koopman Operator Tutorial with Othogonal Polynomials Open
The Koopman Operator (KO) offers a promising alternative methodology to solve ordinary differential equations analytically. The solution of the dynamical system is analyzed in terms of observables, which are expressed as a linear combinati…
View article: Solving ordinary differential equations using Schur decomposition
Solving ordinary differential equations using Schur decomposition Open
This work introduces a methodology to solve ordinary differential equations using the Schur decomposition of the linear representation of the differential equation. This is done by first transforming the system into an upper triangular sys…
View article: Solving ordinary differential equations using Schur decompostion
Solving ordinary differential equations using Schur decompostion Open
This work introduces a methodology to solve ordinary differential equations using the Schur decomposition of the linear representation of the differential equation. This is done by first transforming the system into an upper triangular sys…
View article: Dynamics Near the Three-Body Libration Points via Koopman Operator Theory
Dynamics Near the Three-Body Libration Points via Koopman Operator Theory Open
This paper investigates the application of the Koopman Operator theory to the motion of a satellite about a libration point in the Circular Restricted Three-Body Problem. Recently, the Koopman Operator has emerged as a promising alternativ…
View article: On the Theory of Uniform Satellite Constellation Reconfiguration
On the Theory of Uniform Satellite Constellation Reconfiguration Open
This work focuses on the study of the reconfiguration strategies available for uniformly distributed satellite constellations and slotting architectures. Particularly, this manuscript deals with the cases of reducing, maintaining, and also…
View article: Non-self-intersecting trajectories and their applications to satellite constellation design and orbital capacity
Non-self-intersecting trajectories and their applications to satellite constellation design and orbital capacity Open
This work focuses on the generation of non-self-intersecting relative trajectories, and their applications to satellite constellation design, slotting architectures, and Space Traffic Management. To that end, this paper introduces two theo…
View article: A set of orbital elements to fully represent the zonal harmonics around an oblate celestial body
A set of orbital elements to fully represent the zonal harmonics around an oblate celestial body Open
This work introduces a new set of orbital elements to fully represent the zonal harmonics problem around an oblate celestial body. This new set of orbital elements allows to obtain a linear system for the unperturbed problem and, in additi…
View article: Analytical Solution to the Zonal Harmonics Problem Using Koopman Operator Theory
Analytical Solution to the Zonal Harmonics Problem Using Koopman Operator Theory Open
This work introduces the use of the Koopman Operator Theory to generate analytical solutions for the zonal harmonics problem of a satellite orbiting a non spherical celestial body. Particularly, the solution proposed directly provides the …
View article: Bijective Mapping Analysis to Extend the Theory of Functional Connections to Non-Rectangular 2-Dimensional Domains
Bijective Mapping Analysis to Extend the Theory of Functional Connections to Non-Rectangular 2-Dimensional Domains Open
This work presents an initial analysis of using bijective mappings to extend the Theory of Functional Connections to non-rectangular two-dimensional domains. Specifically, this manuscript proposes three different mappings techniques: (a) c…
View article: Relative and Absolute Station-Keeping for Two-Dimensional–Lattice Flower Constellations
Relative and Absolute Station-Keeping for Two-Dimensional–Lattice Flower Constellations Open
FLOWERconstellations present beautiful and interesting dynamical features that allow exploration of a wide range of potential applications, such as telecommunications, Earth and deep space observation, global positioning systems, and distr…