Related papers: Design of distant retrograde orbits based on a hig…
Ab initio calculations face the challenge of describing a complex multiscale quantum many-body system. The nuclear wave function has both strong short-range correlations and long-range contributions. Natural orbitals provide a means of…
In a previous paper (Gayon & Bois 2008a), we have shown the general efficiency of retrograde resonances for stabilizing compact planetary systems. Such retrograde resonances can be found when two-planets of a three-body planetary system are…
This paper presents an algorithm for the preprocessing of observation data aimed at improving the robustness of orbit determination tools. Two objectives are fulfilled: obtain a refined solution to the initial orbit determination problem…
The main effects of the Earth's oblateness on the motion of artificial satellites are usually derived from the variation of parameters equations of an average representation of the oblateness disturbing function. Rather, we approach their…
Directional data are constrained to lie on the unit sphere of~$\mathbb{R}^q$ for some~$q\geq 2$. To address the lack of a natural ordering for such data, depth functions have been defined on spheres. However, the depths available either…
This paper provides a new approach to derive various arbitrary high order finite difference formulae for the numerical differentiation of analytic functions. In this approach, various first and second order formulae for the numerical…
Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…
The quest of exo-Earths has become a prominent field. In this work, we study the stability of non-coplanar planetary configurations consisting of an inclined inner terrestrial planet in mean-motion resonance with an outer giant planet. We…
Transverse linearization-based approaches have become among the most prominent methods for orbitally stabilizing feedback design in regards to (periodic) motions of underactuated mechanical systems. Yet, in an $n$-dimensional state-space,…
The long-term dynamics of the geostationary Earth orbits (GEO) is revisited through the application of canonical perturbation theory. We consider a Hamiltonian model accounting for all major perturbations: geopotential at order and degree…
We develop two adaptive discretization algorithms for convex semi-infinite optimization, which terminate after finitely many iterations at approximate solutions of arbitrary precision. In particular, they terminate at a feasible point of…
Perturbative analyses of planetary resonances commonly predict singularities and/or divergences of resonance widths at very low and very high eccentricities. We have recently re-examined the nature of these divergences using…
Periodic orbits are important objects of discrete dynamical systems, but finding them is not always easy. We present a self-contained introductory account, aimed at non-experts, to prove their existence and study their stability using the…
Corrections to the relativistic orbits are studied considering higher order approximations induced by gravitomagnetic effects. We discuss in details how such corrections come out taking into account magnetic components in the weak field…
We present a novel analytic extraction of high-order post-Newtonian (pN) parameters that govern quasi-circular binary systems. Coefficients in the pN expansion of the energy of a binary system can be found from corresponding coefficients in…
Recent investigations (e.g. Han et al. 2001) have shown that fitting the Hipparcos observations with an orbital model when the astrometric wobble caused by the companion is below the noise level can have rather unexpected consequences. With…
We introduce the concept of inexact first-order oracle of degree q for a possibly nonconvex and nonsmooth function, which naturally appears in the context of approximate gradient, weak level of smoothness and other situations. Our…
Resolution-Scale Relativity suggests quantum-like dynamics may emerge in chaotic macroscopic systems. In planetary systems, this would lead to orbital periods being proportional to cubed integers $n$. Each system is then characterized by a…
Approximation techniques have been historically important for solving differential equations, both as initial value problems and boundary value problems. The integration of numerical, analytic and perturbation methods and techniques can…
This work develops a functional analytic framework for making computer assisted arguments involving transverse heteroclinic connecting orbits between hyperbolic periodic solutions of ordinary differential equations. We exploit a…