Related papers: Orbit Determination with the two-body Integrals. I…
Cosmological N-body simulations are done on massively parallel computers. This necessitates the use of simple time integrators, and, additionally, of mesh-grid approximations of the potentials. Recently, Adamek et al. (2015);…
We consider the two-body problem in post-Newtonian approximations of general relativity. We report the recent results concerning the equations of motion, and the associated Lagrangian formulation, of compact binary systems, at the third…
We consider systems of ordinary differential equations with known first integrals. The notion of a discrete tangent space is introduced as the orthogonal complement of an arbitrary set of discrete gradients. Integrators which exactly…
The Slater-type orbital basis with non-integer principal quantum numbers is a physically and mathematically motivated choice for molecular electronic structure calculations in both non-relativistic and relativistic theory. The…
By introducing simple topological constraints and applying a binary decomposition method, we show the existence of a set of prograde double-double orbits for any rotation angle $\theta \in (0, \pi/7]$ in the equal-mass four-body problem. A…
We derive a simple analytical expression for the two-body force in a sub-class of MOND-like theories and make testable predictions in the modification to the two-body orbital period, shape, and precession rate, and escape speed etc. We…
The increasing volume of space objects in Earth's orbit presents a significant challenge for Space Situational Awareness (SSA). And in particular, accurate orbit prediction is crucial to anticipate the position and velocity of space…
We reduce two-body problem to the one-body problem in general case of deformed Heisenberg algebra leading to minimal length.Two-body problems with delta and Coulomb-like interactions are solved exactly. We obtain analytical expression for…
We revisit the relativistic restricted two-body problem with spin employing a perturbation scheme based on Lie series. Starting from a post-Newtonian expansion of the field equations, we develop a first-order secular theory that reproduces…
In this work we investigate the presence of defect structures in models described by two real scalar fields. The coupling between the two fields is inspired on the equations for a multimode laser, and the minimum energy trivial…
An efficient geometric integrator is proposed for solving the perturbed Kepler motion. This method is stable and accurate over long integration time, which makes it appropriate for treating problems in astrophysics, like solar system…
After some more than four centuries from the formulation and publication (in Astronomia Nova) of the Kepler's Equation, which relates the eccentric (and, intermediately, the true) anomaly of the planetary trajectories to the uniformly…
Short-arc orbit determination is crucial when an asteroid is first discovered. In these cases usually the observations are so few that the differential correction procedure may not converge. We have developed an initial orbit computation…
A common problem in physics and engineering is determination of the orientation of an object given its angular velocity. When the direction of the angular velocity changes in time, this is a nontrivial problem involving coupled differential…
We derive the second-order post-Minkowskian solution for the small-deflection motion of test particles in the external field of the Kerr-Newman black hole via an iterative method. The analytical results are exhibited in the coordinate…
The quantitative characterization of amplitudes and periods of perturbations in orbital elements can help to our understanding the minor bodies dynamics, especially in case motion in vicinity of resonances. The main goal of this study is to…
We determine the conductivity of the interior of a body using electrical measurements on its surface. We assume only that the conductivity is bounded below by a positive constant and that the conductivity and surface are Lipschitz…
We will make the case that \textit{pedal coordinates} (instead of polar or Cartesian coordinates) are more natural settings in which to study force problems of classical mechanics in the plane. We will show that the trajectory of a test…
Planet formation is often considered in the context of one circumstellar disk around one star. Yet stellar binary systems are ubiquitous, and thus a substantial fraction of all potential planets must form and evolve in more complex,…
We study the orbits of two interacting particles described by a fully relativistic classical mechanical Hamiltonian. We use two sets of initial conditions. In the first set (dynamics 1) the system's center of mass is at rest. In the second…