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Quaternion Regularization of Singularities of Astrodynamics Models Generated by Gravitational Forces (Review)
AbstractThe article presents an analytical review of works devoted to the quaternion regularization of the singularities of differential equations of...
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Orbit transfer using Theory of Functional Connections via change of variables
This work shows that a class of astrodynamics problems subject to mission constraints can be efficiently solved using the Theory of Functional...
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Quaternion Methods and Regular Models of Celestial Mechanics and Space Flight Mechanics: The Use of Euler (Rodrigues–hamilton) Parameters to Describe Orbital (Trajectory) Motion. I: Review and Analysis of Methods and Models and Their Applications
AbstractThe problem of regularization of the classical equations of celestial mechanics and space flight mechanics (astrodynamics) is considered, in...
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Quaternion and Biquaternion Methods and Regular Models of Analytical Mechanics (Review)
AbstractThis paper is an analytical review in which we present quaternion and biquaternion methods for describing motion, models of the theory of...
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Quaternion Methods and Regular Models of Celestial and Space Flight Mechanic: Using Euler (Rodrigues–Hamilton) Parameters to Describe Orbital (Trajectory) Motion. II: Perturbed Spatial Restricted Three-Body Problem
AbstractThe article considers the problem of regularizing the features of the classical equations of celestial mechanics and space flight mechanics...
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Inertial Navigation in Space Using the Regular Quaternion Equations of Astrodynamics
Quaternion equations are proposed for the ideal operation of spatial inertial navigation systems with an azimuthally stabilized platform and a...
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Okhotsimsky-Egorov Method for Solving the Euler-Lambert Problem
A method for solving the Euler-Lambert problem by V.A. Egorov is presented, based on the work of D.E. Okhotsimsky and on the analysis of a set of...
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Physics-informed neural networks for gravity field modeling of the Earth and Moon
High-fidelity representations of the gravity field underlie all applications in astrodynamics. Traditionally these gravity models are constructed...
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Quaternion Regularization of Differential Equations of Perturbed Central Motion and Regular Models of Orbital (Trajectory) Motion: Review and Analysis of Models, Their Applications
AbstractThe review article briefly outlines our proposed general quaternion theory of regularizing and stabilizing transformations of Newtonian...
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Nonlinear orbital uncertainty propagation with differential algebra and Gaussian mixture model
Nonlinear uncertainty propagation is of critical importance in many application fields of astrodynamics. In this article, a framework combining the...
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An identifier-actor-optimizer policy learning architecture for optimal control of continuous-time nonlinear systems
An intelligent solution method is proposed to achieve real-time optimal control for continuous-time nonlinear systems using a novel...
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An investigation on space debris of unknown origin using proper elements and neural networks
Proper elements represent a dynamical fingerprint of an object’s inherent state and have been used by small-body taxonomists in characterizing...
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Nonlinear representation of the confidence region of orbits determined on short arcs
The total number of active satellites, rocket bodies, and debris larger than 10 cm is currently about 20,000. If all resident space objects larger...
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Prediction and Correction of the Orbital Motion of Spacecraft using Regular Quaternion Equations and Their Solutions in the Kustaanheimo–Stiefel Variables and Isochronic Derivatives
AbstractThe regular quaternion equations of the orbital motion of a spacecraft (SC) proposed by us earlier in four-dimensional Kustaanheimo–Stiefel...
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Comparison of continuity equation and Gaussian mixture model for long-term density propagation using semi-analytical methods
This paper compares the continuum evolution for density equation modelling and the Gaussian mixture model on the 2D phase space long-term density...
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Celestial mechanics: new discoveries and challenges for space exploration
This special issue entitled “Celestial Mechanics: New Discoveries and Challenges for Space Exploration” presents a series of 27 contributions. Some...
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Coplanar circular-to-circular orbit transfer guidance with constant-thrust acceleration
A semi-analytical solution for circular-to-circular planar orbit transfers is presented. In particular, the problem is addressed with a judiciously...
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A novel analytic continuation power series solution for the perturbed two-body problem
Inspired by the original developments of recursive power series by means of Lagrange invariants for the classical two-body problem, a new analytic...
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Low-Thrust Trajectory Optimization in Kustaanheimo–Stiefel Variables
AbstractThe regularization of spacecraft motion equations by the Kustaanheimo–Stiefel transformation for coordinates and Sundman’s transformation for...
