Related papers: Earth satellite dynamics by Picard iterations
In the current study, a double-averaged analytical model including the action of the perturbing body's inclination is developed to study third-body perturbations. The disturbing function is expanded in the form of Legendre polynomials…
The acclaimed merits of analytical solutions based on a fictitious time developed in the 1970's were partially overvalued due to a common misuse of classical analytical solutions based on the physical time that were taken as reference. With…
The Galilean satellites' dynamics has been studied extensively during the last century. In the past it was common to use analytical expansions in order to get simple models to integrate, but with the new generation computers it became…
An approach is treated for numerical integration of ordinary differential equations systems of the first order with choice of a computation scheme, ensuring the required local precision. The treatment is made on the basis of schemes of…
This work shows the dynamical instability that can happen to close-in satellites when planet oblateness is not accounted for in non-coplanar multiplanet systems. Simulations include two secularly interacting Jupiter-mass planets mutually…
The navigation satellite constellations in medium-Earth orbit exist in a background of third-body secular resonances stemming from the perturbing gravitational effects of the Moon and the Sun. The resulting chaotic motions, emanating from…
We study the resonant dynamics in a simple one degree of freedom, time dependent Hamiltonian model describing spin-orbit interactions. The equations of motion admit periodic solutions associated with resonant motions, the most important…
The dynamical features of the irregular satellites of the giant planets argue against an in-situ formation and are strongly suggestive of a capture origin. Since the last detailed investigations of their dynamics, the total number of…
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…
Solution of Ordinary Differential Equation (ODE) model of dynamical system may not agree with its observed values. Often this discrepancy can be attributed to unmodeled forcings in the evolution rule of the dynamical system. In this…
The work considers the design of an indirect adaptive controller for a satellite equipped with a robotic arm manipulating an object. Uncertainty on the manipulated object can considerably impact the overall behavior of the system. In…
A popular intermediary in the theory of artificial satellites is obtained after the elimination of parallactic terms from the J2-problem Hamiltonian. The resulting quasi-Keplerian system is in turn converted into the Kepler problem by a…
For solving linear ill-posed problems regularization methods are required when the right hand side is with some noise. In the present paper regularized solutions are obtained by implicit iteration methods in Hilbert scales. % By exploiting…
The project consists to determine, mathematically, the trajectory that will take an artificial satellite to fight against the air resistance. During our work, we had to consider that our satellite will crash to the surface of our planet. We…
Numerical simulations carried out over the past decade suggest that the orbits of the Global Navigation Satellite Systems are unstable, resulting in an apparent chaotic growth of the eccentricity. Here we show that the irregular and…
A highly precise model for the motion of a rigid Earth is indispensable to reveal the effects of non-rigidity in the rotation of the Earth from observations. To meet the accuracy goal of modern theories of Earth rotation of 1 microarcsecond…
In this article we have studied the controllability of artificial satellite under the effect of zonal harmonic $J_2$ in cylindrical polar coordinates systems. Seven different cases of thrusters in various directions have been analyzed and…
The conjecture is considered that every body induces the wave field which imposes oscillations on the gravitational potential of a body. The function for oscillations is chosen to prevent the gravitational collapse of the matter at the…
Irregular satellites (IS) are believed to have been captured during the Solar system's dynamical history and provide clues for the Solar system's formation and evolution. IS occupy a large fraction of the Hill sphere of their host planet…
We consider a nearly free falling Earth satellite where atomic wave interferometers are tied to a telescope pointing towards a faraway star. They measure the acceleration and the rotation relatively to the local inertial frame. We calculate…