arXiv subjects

A. K. de Almeida Jr

Publications and source records attributed to A. K. de Almeida Jr.

4 recordsLinked to original sources

arXiv2026

A generalized dipole-segment model for the gravitational field of elongated bodies

Context. Various simplified models have been investigated to understand the complex dynamical environment near irregular asteroids. We propose a generalized dipole-segment model (GDSM) to describe the gravitational fields of elongated bodies. The proposed model extends the dipole-segment model (DSM) by including variable pole masses and a connecting rod while also accounting for the spheroidal shape of the poles instead of assuming point masses. Methods. A nonlinear optimization method was employed to determine the model parameters, which minimizes the errors between the equilibrium points predicted by the GDSM and those obtained using a more realistic approach, such as the polyhedron model, which is assumed to provide the accurate values of the system. The model was applied to three real irregular bodies: the Kuiper belt objects Arrokoth, Kleopatra, and comet 103P/Hartley. Results. The results show that the GDSM represents the gravitational field more accurately than the DSM and significantly reduces computational time and effort when compared with the polyhedron model. This reduction in computational complexity does not come at the cost of efficiency. This makes the GDSM a valuable tool for practical applications. The model was further employed to compute heteroclinic orbits that connect the unstable triangular equilibrium points of the system. These trajectories, obtained from the intersections of the stable and unstable manifolds, represent natural pathways that enable transfers between equilibrium regions without continuous propulsion. The results for Arrokoth, Kleopatra, and 103P/Hartley are consistent and validate the GDSM as an accurate and computationally efficient framework for studying the dynamical environment and transfer mechanisms around irregular small bodies.

astro-ph.EP↗

arXiv2025

Poincaré Maps with the Theory of Functional Connections

Poincaré maps play a fundamental role in nonlinear dynamics and chaos theory, offering a means to reduce the dimensionality of continuous dynamical systems by tracking the intersections of trajectories with lower-dimensional section surfaces. Traditional approaches typically rely on numerical integration and interpolation to detect these crossings, which can lead to inaccuracies and computational inefficiencies. This work presents a novel methodology for constructing Poincaré maps based on the Theory of Functional Connections (TFC). The constrained functionals produced by TFC yield continuous and differentiable representations of system trajectories that exactly satisfy prescribed constraints. The computation of Poincaré maps is formulated as either an initial value problem (IVP) or a boundary value problem (BVP). For IVPs, initial conditions are embedded into the functional, and the intersection time with a specified section surface is determined. We demonstrate linear convergence to the Taylor series, thereby enabling accurate interpolation without resorting to numerical integration or external optimization. For BVPs, periodicity conditions are encoded to identify periodic orbits in a Three-Body Problem context. Furthermore, by enforcing periodic constraints, we show how to construct first recurrence maps. The methodology is also extended to non-autonomous systems, demonstrated through applications to a Four-Body Problem. The proposed approach achieves machine-level accuracy with modest computational effort, eliminating the need for variable transformations or iterative integration schemes with adaptive step-sizing. The results illustrate that TFC offers a powerful and efficient alternative framework for constructing Poincaré maps, computing periodic orbits, and analyzing complex dynamical systems, particularly in astrodynamical contexts.

astro-ph.IM↗

arXiv2025

Connecting Earth and Moon via the L1 Lagrangian point

The renewed global interest in lunar exploration requires new orbital strategies to ensure flight safety which can benefit extended lunar missions and service a plethora of planned instruments in the lunar orbit and surface. We investigate here the equivalent fuel consumption cost to transfer from (to) a given orbit and enter (leave) at any point of an invariant manifold associated with a Lyapunov orbit around the Earth-Moon $L_1$ Lagrangian point using bi-impulsive maneuvers. Whereas solving this type of transfer is generally computationally expensive, we simulate here tens of millions of transfers orbits, for different times of flight, Jacobi constants and spatial location on the manifold. We are able to reduce computational cost by taking advantage of the efficient procedure given by the Theory of Functional Connections for solving boundary value problems, represented with special constraints created to the purposes of this work. We develop here the methodology for constructing these transfers, and apply it to find a low-cost transfer from an orbit around the Earth to a stable manifold and another low-cost transfer from an unstable manifold to an orbit around the Moon. In the end, we obtain an innovative Earth-to-Moon transfer that involves a gravity assist maneuver with the Moon and allows a long stationed stage at the Lyapunov orbit around $L_1$ which can be used for designing multi-purpose missions for extended periods of time with low fuel costs. This is paramount to optimize new exploration concepts.

astro-ph.IM↗

arXiv2023

Analysis of the dynamics of a spacecraft in the vicinity of an asteroid binary system with equal masses

In this work, we performed a dynamical analysis of a spacecraft around a nearly equal-mass binary near-Earth asteroid with application to the asteroid 2017 YE5, which is also a possible dormant Jupiter-family comet. Thus, we investigated the motion of a particle around this binary system using the circular restricted three-body problem. We calculated the locations of the Lagrangian points of the system and their Jacobi constant. Through numerical simulations, using the Poincaré Surface of Sections, it was possible to find several prograde and retrograde periodic orbits around each binary system's primary, some exhibiting significantly-sized higher-order behavior. We also calculated the stability of these orbits. After finding the periodic orbits, we investigated the influence of solar radiation pressure on these orbits. For this analysis, we considered that the area-to-mass ratio equals 0.01 and 0.1. We also performed a spacecraft lifetime analysis considering the physical and orbital characteristics of the 2017YE5 system and investigated the behavior of a spacecraft in the vicinity of this system. We analyzed direct and retrograde orbits for different values of Jacobi's constant. This study investigated orbits that survive for at least six months, not colliding or escaping the system during that time. We also analyze the initial conditions that cause the spacecraft to collide with $M_1$ or $M_2$, or escape from the system. In this work, we take into account the gravitational forces of the binary asteroid system and the solar radiation pressure (SRP). Finally, we calculated optimal bi-impulsive orbital maneuvers between the collinear Lagrangian points. We found a family of possible orbital transfers considering times of flight between 0.1 and 1 day.

astro-ph.EP↗