Related papers: A new correction method for quasi-Keplerian orbits
We are interested in the classical ill-posed Cauchy problem for the Laplace equation. One method to approximate the solution associated with compatible data consists in considering a family of regularized well-posed problems depending on a…
Extending many-body numerical techniques which are powerful in the context of simple model calculations to the realm of realistic material simulations can be a challenging task. Realistic systems often involve multiple active orbitals,…
In the restricted four-body problem consisting of the Earth, the Moon and the Sun as the primaries and a spacecraft as the planetoid, we take into account the solar perturbation in the description of the motion of a spacecraft in the…
The dominantly orbital state method allows a semiclassical description of quantum systems. At the origin, it was developed for two-body relativistic systems. Here, the method is extended to treat two-body Hamiltonians and systems with three…
Reparameterization from the standard set of orbital elements to Cartesian position-velocity vectors can be computationally advantageous for orbit inference problems, particularly when orbital elements are weakly constrained. Here we present…
The relativistic 2-body problem, much like the non-relativistic one, is reduced to describing the motion of an effective particle in an external field. The concept of a relativistic reduced mass and effective particle energy introduced some…
We use the recently introduced single-particle states obtained from localized Deuteron wave-functions as a basis for nuclear many-body calculations. We show that energies can be substantially lowered if the natural orbits obtained from this…
We consider two different relativistic versions of the Kepler problem in the plane: the first one involves the relativistic differential operator, the second one involves a correction for the usual gravitational potential due to…
We study a 2-body problem given by the sum of the Newtonian potential and an anisotropic perturbation that is a homogeneous function of degree $-\beta$, $\beta\ge 2$. For $\beta>2$, the sets of initial conditions leading to…
We study relativistic Kepler problems in the plane. At first, using non-smooth critical point theory, we show that under a general time-periodic external force of gradient type there are two infinite families of T-periodic solutions,…
Detailed numerical analyses of the orbital motion of a test particle around a spinning primary are performed. They aim to investigate the possibility of using the post-Keplerian (pK) corrections to the orbiter's periods (draconitic,…
Two-loop corrections with scalar and vector form factors are calculated for nuclear matter in the Walecka model. The on-shell form factors are derived from vertex corrections within the framework of the model and are highly damped at large…
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…
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…
The conservation of energy, linear momentum and angular momentum are important drivers for our physical understanding of the evolution of the Universe. These quantities are also conserved in Newton's laws of motion under gravity…
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…
The 2:1 mean motion resonance orbit was integrated at the restricted planar 3-body problem in absolute frame. Orbit of Jupiter was assumed circular. Initial Jupiter longitude was assumed zero. The Runge-Kutta method was used. The start of…
We construct a Nekhoroshev-like result of stability with sharp constants for the planar three body problem, both in the planetary and in the restricted circular case, by using the periodic averaging technique. Our constructions can be…
As shown by Johannes Kepler in 1609, in the two-body problem, the shape of the orbit, a given ellipse, and a given non-vanishing constant angular momentum determines the motion of the planet completely. Even in the three-body problem, in…
We develop a new inexact interior-point Lagrangian decomposition method to solve a wide range class of constrained composite convex optimization problems. Our method relies on four techniques: Lagrangian dual decomposition, self-concordant…