Related papers: A Novel Orbit Parameterization in Spherical Coordi…
We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we…
A trajectory isomorphism between the two Newtonian fixed center problem in the sphere and two associated planar two fixed center problems is constructed by performing two simultaneous gnomonic projections in $S^2$. This isomorphism converts…
The goal of the present paper is to make a numerical analysis of parametric optimization of low thrust orbital maneuver. An orbital maneuver occurs when it is necessary to modify the orbit a space vehicle to change its function or to…
In this paper we study paramertized motion planning algorithms which provide universal and flexible solutions to diverse motion planning problems. Such algorithms are intended to function under a variety of external conditions which are…
We give a method to determine relative periodic orbits in point vortex systems: it consists mainly into perform a symplectic reduction on a fixed point submanifold in order to obtain a two-dimensional reduced phase space. The method is…
We develop a direct geometric method to determine the orbital parameters and mass of a planet, and we then apply the method to Neptune using high-precision data for the other planets in the solar system. The method is direct in the sense…
The concept of sphere of influence of a planet is useful in both the context of impact monitoring of asteroids with the Earth and of the design of interplanetary trajectories for spacecrafts. After reviewing the classical results, we…
Spacecraft formation flying serves as a method of astronomical instrumentation that enables the construction of large virtual structures in space. The formation-flying interferometry generally requires very-high control accuracy, and…
Surface parameterization is a fundamental concept in fields such as differential geometry and computer graphics. It involves mapping a surface in three-dimensional space onto a two-dimensional parameter space. This process allows for the…
The purpose of this paper is to explore a new way of autonomous mapping. Current systems using perception techniques like LAZER or SONAR use probabilistic methods and have a drawback of allowing considerable uncertainty in the mapping…
We propose a new algorithm, for parameter estimation that is applicable to imaging using moving and synthetic aperture arrays. The new method results in higher resolution and more accurate estimation than commonly used methods when strong…
We discuss how the kernel convolution approach can be used to accurately approximate the spatial covariance model on a sphere using spherical distances between points. A detailed derivation of the required formulas is provided. The proposed…
We provide a fast algorithm to diagnose any directional dependence in the cosmological parameters by calculating maps of local cosmological parameter estimates and their joint errors. The technique implements a fast quadratic estimator…
Smooth parametrization consists in a subdivision of the mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the…
We present a Bayesian algorithm to combine optical imaging of unresolved objects from distinct epochs and observation platforms for orbit determination and tracking. By propagating the non-Gaussian uncertainties we are able to optimally…
Isolated horizon conditions specialized to spherical symmetry can be imposed directly at the quantum level. This answers several questions concerning horizon degrees of freedom, which are seen to be related to orientation, and its…
We present a novel numerical method to calculate periodic orbits for dynamical systems by an iterative process which is based directly on the action integral in classical mechanics. New solutions are obtained for the planar motion of three…
Spectral analysis of open surfaces is gaining momentum for studying surface morphology in engineering, computer graphics, and medical domains. This analysis is enabled using proper parameterization approaches on the target analysis domain.…
While building up a catalog of Earth orbiting objects, if the available optical observations are sparse, not deliberate follow ups of specific objects, no orbit determination is possible without previous correlation of observations obtained…
We describe an analytical method for computing the orbital parameters of a planet from the periodogram of a radial velocity signal. The method is very efficient and provides a good approximation of the orbital parameters. The accuracy is…