Related papers: Non-averaged regularized formulations as an altern…
This paper is related to our previous works [1][2] on the error estimate of the averaging technique, for systems with one fast angular variable. In the cited references, a general method (of mixed analytical and numerical type) has been…
Numerical integration of orbit trajectories for a large number of initial conditions and for long time spans is computationally expensive. Semi-analytical methods were developed to reduce the computational burden. An elegant and widely used…
We present a fully analytical propagator for the orbits of lunar artificial satellites in a lunar gravity and third-body model sufficiently precise for a wide range of practical applications. The gravity model includes the twelve most…
The present report summarizes the main theory and implementation steps associated with SELENA (SEmi-anaLytical intEgrator for a luNar Artificial satellite), i.e. the semi-analytical propagator for lunar satellite orbits developed in the…
This paper presents a regularization technique incorporating a non-convex and non-smooth term, $\ell_{1}^{2}-\eta\ell_{2}^{2}$, with parameters $0<\eta\leq 1$ designed to address ill-posed linear problems that yield sparse solutions. We…
We extend some previous results of our work [1] on the error of the averaging method, in the one-frequency case. The new error estimates apply to any separating family of seminorms on the space of the actions; they generalize our previous…
Modern parabolic equation (PE) methods for wave propagation rely on application of a variety of fractional-powered differential operators. Rational approximations of these operators need to properly map their spectra onto the complex plane,…
We present a new iterative rotation inversion technique based on the Simultaneous Algebraic Reconstruction Technique developed for image reconstruction. We describe in detail our algorithmic implementation and compare it to the classical…
In this work we present a new methodology for orbit propagation, the hybrid perturbation theory, based on the combination of an integration method and a prediction technique. The former, which can be a numerical, analytical or…
We present STEEL a STatistical sEmi-Empirical modeL designed to probe the distribution of satellite galaxies in groups and clusters. Our fast statistical methodology relies on tracing the abundances of central and satellite haloes via their…
This paper addresses the computation of Delta-V-optimal, safe, relative orbit reconfigurations for satellite formations in a centralized fashion. The formations under consideration comprise an uncontrolled chief spacecraft flying with an…
Normal form stability estimates are a basic tool of Celestial Mechanics for characterizing the long-term stability of the orbits of natural and artificial bodies. Using high-order normal form constructions, we provide three different…
This study presents a fast nonlinear programming algorithm for low-thrust multi-asteroid rendezvous missions. The core contribution is the derivation of analytical formulations for both first- and second-order gradients of low-thrust…
Low Earth orbit (LEO) satellites are leveraged to support new position, navigation, and timing (PNT) service alternatives to GNSS. These alternatives require accurate propagation of satellite position and velocity with a realistic…
This paper presents an analytical model for collision probability assessments between de-orbiting or injecting space objects and satellite constellations. Considering the first to be subjected to a continuous tangential acceleration, its…
In this paper, we develop a regularized higher-order Taylor based method for solving composite (e.g., nonlinear least-squares) problems. At each iteration, we replace each smooth component of the objective function by a higher-order Taylor…
We provide a primer to numerical methods based on Taylor series expansions such as generalized finite difference methods and collocation methods. We provide a detailed benchmarking strategy for these methods as well as all data files…
This work develops an analytical framework for downlink low Earth orbit (LEO) or medium Earth orbit (MEO) satellite communications, leveraging tools from stochastic geometry. We propose a tractable approach to the analysis of such satellite…
We describe a proof-of-concept development and application of a phase averaging technique to the nonlinear rotating shallow water equations on the sphere, discretised using compatible finite element methods. Phase averaging consists of…
The auxiliary functions provide efficient computation of integrals arising at the self-consistent field (SCF) level for molecules using Slater-type bases. This applies both in relativistic and non-relativistic electronic structure theory.…