Related papers: Geometric Perspectives on Fundamental Solutions in…
We expand the solutions of linearly coupled Mathieu equations in terms of infinite-continued matrix inversions, and use it to find the modes which diagonalize the dynamical problem. This allows obtaining explicitly the ('Floquet-Lyapunov')…
It is believed that some numerical technique must be employed for the determination of the system parameters of a visual binary or a star with a planet because the relevant equations are not only highly nonlinear but also transcendental…
We propose a methodology to study the bifurcation sequences of frozen orbits when the 2nd-order fundamental model of the satellite problem is augmented with the contribution of octupolar terms and relativistic corrections. The method is…
This paper presents an adaptive observer-based navigation strategy for spacecraft in Circular Relative Orbit (CRO) scenarios, addressing challenges in proximity operations like formation flight and uncooperative target inspection. The…
This article produces wave equations and constructs traveling wave solutions that are intimately related to Newton's equations of celestial mechanics. The traveling wave solutions are expressed in ``closed form'' in terms of elementary…
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…
In this paper, a surface geometric constraint approach is used in designing the orbits of a solar sail. We solve the solar sail equation of motion by obtaining a generalized Laplace-Runge-Lenz (LRL) vector with the assumption that the cone…
This paper explores transverse coordinates for the purpose of orbitally stabilizing periodic motions of nonlinear, control-affine dynamical systems. It is shown that the dynamics of any (minimal or excessive) set of transverse coordinates,…
When dealing with satellites orbiting a central body on a highly elliptical orbit, it is necessary to consider the effect of gravitational perturbations due to external bodies. Indeed, these perturbations can become very important as soon…
Many alternative theories of gravity screens a Yukawa-type potential. This article shows Keplerian-type parametrization as a solution of Yukawa type potential accurate equations of motion for two non-spinning compact objects moving in an…
We are reinvestigating the hyperfine structure of sodium using a fully relativistic multiconfiguration approach. In the fully relativistic approach, the computational strategy somewhat differs from the original nonrelativistic counterpart…
In this paper we present a framework which provides an analytical (i.e., infinitely differentiable) transformation between spatial coordinates and orbital elements for the solution of the gravitational two-body problem. The formalism omits…
We develop a linear method for solving the nonlinear differential equations of a lumped-parameter thermal model of a spacecraft moving in a closed orbit. Our method, based on perturbation theory, is compared with heuristic linearizations of…
This study presents autonomous guidance and control strategies for the purpose of reconfiguring close-range multi-satellite formations. The formation under consideration includes $N$ under-actuated deputy satellites and an uncontrolled…
This work introduces a linearized analytical model for the study of the dynamic of satellites in near circular orbits under the effects of the atmospheric drag. This includes the evaluation of the station keeping required for each satellite…
A high order optimal control strategy implemented in the Koopman operator framework is proposed in this work. The new technique exploits the Koopman representation of the solution of the equations of motion to develop an energy optimal…
Today, the motion of spacecrafts is still described according to the classical Newtonian equations plus the so-called "relativistic corrections", computed with the required precision using the Post-(Post-)Newtonian formalism. The current…
The authors try to find a good solution of an artificial satellite motion under the influence of J2 gravity in terms of KS variables by using Picard Iterative Method. The result shows that there are many solutions for this problem depends…
Accurate orbit modeling plays a key role in contemporary and future space missions such as GRACE and its successor GRACE-FO, GNSS, and altimetry missions. To fully exploit the technological capabilities and correctly interpret measurements,…
We show the traditional rocket problem, where the ejecta velocity is assumed constant, can be reduced to an integral quadrature of which the completely non-relativistic equation of Tsiolkovsky, as well as the fully relativistic equation…