Related papers: Orbital Acceleration Using Product of Exponentials
We develop a computational approach for calculating the optical conductivity in the augmented plane wave basis set of Wien2K and apply it for thoroughly comparing the full dipole matrix element calculation and the Peierls approximation. The…
The tracer equations are part of the primitive equations used in ocean modeling and describe the transport of tracers, such as temperature, salinity or chemicals, in the ocean. Depending on the number of tracers considered, several…
The minimum orbital intersection distance is used as a measure to assess potential close approaches and collision risks between astronomical objects. Methods to calculate this quantity have been proposed in several previous publications.…
To manipulate orbital angular momentum (OAM) carried by light beams, there is a great interest in designing various optical elements from the deep-ultraviolet to the microwave. Normally, the OAM variation introduced by optical elements can…
We study the general relativistic orbital equation and using a straightforward perturbation method and a mathematical device first introduced by d'Alembert, we work out approximate expressions of a bound planetary orbit in the form of…
Methods for calculating an electron density of a periodic crystal constructed using non-orthogonal localised orbitals are discussed. We demonstrate that an existing method based on the matrix expansion of the inverse of the overlap matrix…
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…
We consider the motion of uncharged dust grains of arbitrary shape including the effects of electromagnetic radiation and thermal emission. The resulting relativistically covariant equation of motion is expressed in terms of standard…
It is shown that orbital period ratios of successive secondaries in the Solar planetary and giant satellite systems and in exoplanetary systems are preferentially closer to irreducible fractions formed with Fibonacci numbers between 1 and 8…
A new, second-order solution in curvilinear coordinates is introduced for the relative motion of two spacecraft on eccentric orbits. The second-order equations for unperturbed orbits are derived in spherical coordinates with true anomaly as…
In this thesis are shown developments in the random phase approximation (RPA) in the context of range-separated theories. We present advances in the formalism of the RPA in general, and particularly in the "dielectric matrix" formulation of…
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…
Previously a mathematical approach has been developed for calculation of the propagation time of a signal, emitted by a moving along an elliptical orbit satellite, with account also for the General Relativity Theory (GRT) effects. The…
The mechanics of an oriented point (point with "spin") based on 3D and 4D Frenet equations is considered. In such mechanics there is an opportunity to describe formally any physical trajectory of a particle with own rotation. We use…
We develop a theoretical framework for the calculation of orbits for a system consisting of a spherical object and a non-spherical body, which is then specialized to a prolate ellipsoid. Particular trajectories are presented that illustrate…
The optimized effective potential (OEP) is the exact Kohn-Sham potential for explicitly orbital-dependent energy functionals, e.g., the exact exchange energy. We give a proof for the OEP equation which does not depend on the chain rule for…
The general tensorial form of the orbit-orbit interaction operator in the formalism of second quantization is presented. Such an expression is needed to calculate both diagonal and off-diagonal matrix elements with respect to…
Planetary, stellar and galactic physics often rely on the general restricted gravitational N-body problem to model the motion of a small-mass object under the influence of much more massive objects. Here, I formulate the general restricted…
The Partial Integral Equation (PIE) framework was developed to computationally analyze linear Partial Differential Equations (PDEs) where the PDE is first converted to a PIE and then the analysis problem is solved by solving operator-valued…
Starting from the Hamiltonian representation of the dynamics in \cite{rosengren2015chaos,colombo2019long}, this work proposes an innovative procedure to design fully-analytical maneuvers for post-mission disposal of HEOs satellites,…