相关论文: A numerical solution of the inverse problem in cla…

A method for asteroid deflection that makes use of a spacecraft moving back and forth on a segment of a Keplerian orbit about the asteroid is studied with the aim of optimizing the initial gross mass of the spacecraft. The corresponding…

During recent decades, there has been a substantial development in optimal mass transport theory and methods. In this work, we consider multi-marginal problems wherein only partial information of each marginal is available, which is a setup…

Orbital parameters of planets are fitted directly to an appropriate set of observations. It is shown how to use the rigorous Deming method combined with a numerical integration of gravitation equations. In all, 65 parameters of the nine…

Planetary-scale collisions are common during the last stages of formation of solid planets, including the Solar system terrestrial planets. The problem of growing planets has been divided into studying the gravitational interaction of…

Piecewise constant curvature is a popular kinematics framework for continuum robots. Computing the model parameters from the desired end pose, known as the inverse kinematics problem, is fundamental in manipulation, tracking and planning…

There are periodic solutions to the equal-mass three-body (and N-body) problem in Newtonian gravity. The figure-eight solution is one of them. In this paper, we discuss its solution in the first and second post-Newtonian approximations to…

In this work numerical methods for solving Einstein's equations are developed and applied to the study of inhomogeneous cosmological models. A two-dimensional computer code is described which implements two advanced numerical methods:…

A metric-field approach to gravitation is presented. It is based on an idea of dependency of space-time properties on measuring instruments. Some bimetric equations that realize this idea are considered. They were tested by the binary…

We introduce new methods for the numerical solution of general Hamiltonian boundary value problems. The main feature of the new formulae is to produce numerical solutions along which the energy is precisely conserved, as is the case with…

The motion of Mercury using numerical methods in the framework of a model including only the non-relativistic Newtonian gravitational interactions of the solar system, 9 planets in translation (including Pluto) around the sun has been…

We use the corrections to the Newton-Einstein secular precessions of the longitudes of perihelia of some planets (Mercury, Earth, Mars, Jupiter, Saturn) of the Solar System, phenomenologically estimated as solve-for parameters by the…

We discuss the influence of the cosmological constant $\Lambda$ on the gravitational equations of motion of bodies with arbitrary masses and eventually solve the two-body problem. Observational constraints are derived from measurements of…

We consider many-body problems in classical mechanics where a wide range of time scales limits what can be computed. We apply the method of optimal prediction to obtain equations which are easier to solve numerically. We demonstrate by…

A pure two-body problem has seven integrals including the Kepler energy, the Laplace vector, and the angular momentum vector. However, only five of them are independent. When the five independent integrals are preserved, the two other…

An optimization program is used to re-adjust the initial conditions, in order to reproduce as closely as possible the predictions of a complete ephemeris by using simplified equations of motion in the numerical integration. The adjustment…

Despite the huge number of research into the three-body problem in physics and mathematics, the study of this problem still remains relevant both from the point of view of its broad application and taking into account its fundamental…

Using a variational method, we exhibit a surprisingly simple periodic orbit for the newtonian problem of three equal masses in the plane. The orbit has zero angular momentum and a very rich symmetry pattern. Its most surprising feature is…

The work is devoted to the critical analysis of theoretical prediction and astronomical observation of GR effects, first of all, the Mercury's perihelion advance. In the first part, the methodological issues of observations are discussed…

We present a three-point inverse solution for reconstructing meteoroid deceleration and mass-loss histories from sparse observations constrained only by the entry, peak-brightness, and terminal points. The method combines the…

An understanding of how input parameter uncertainty in the numerical simulation of physical models leads to simulation output uncertainty is a challenging task. Common methods for quantifying output uncertainty, such as performing a grid or…