The perturbed three-dimensional two body problem: regular quaternion equations of relative motion

2018 ◽  
Vol 82 (6) ◽  
pp. 721-733
Author(s):  
Yu. Chelnokov ◽  
Keyword(s):  
Relative Motion ◽  
Body Problem ◽  
Three Dimensional ◽  
Two Body Problem

Three-Dimensional Formulation of the Relativistic Two-Body Problem

1973 ◽  
pp. 69-109 ◽  
Author(s):  
V. G. Kadyshevskii ◽  
R. M. Mir-Kasimov ◽  
N. B. Skachkov
Keyword(s):  
Body Problem ◽  
Three Dimensional ◽  
Two Body Problem

Three-dimensional formulation of the relativistic two-body problem in terms of rapidities

1977 ◽  
Vol 30 (3) ◽  
pp. 212-221 ◽  
Author(s):  
I. V. Amirkhanov ◽  
G. V. Grusha ◽  
R. M. Mir-Kasimov
Keyword(s):  
Body Problem ◽  
Three Dimensional ◽  
Two Body Problem

scholarly journals NUMERICAL METHODS FOR THE THREE-DIMENSIONAL TWO-BODY PROBLEM IN THE ACTION-AT-A-DISTANCE ELECTRODYNAMICS

2001 ◽  
Vol 12 (05) ◽  
pp. 739-750 ◽  
Author(s):  
I. N. NIKITIN ◽  
J. DE LUCA
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Body Problem ◽  
Three Dimensional ◽  
Deviating Arguments ◽  
Iterative Schemes ◽  
Two Body Problem ◽  
High Energies ◽  
Extrapolation Formula ◽  
Action At A Distance

We develop two numerical methods to solve the differential equations with deviating arguments for the motion of two charges in the action-at-a-distance electrodynamics. Our first method uses Stürmer's extrapolation formula and assumes that a step of integration can be taken as a step of light ladder, which limits its use to shallow energies. The second method is an improvement of pre-existing iterative schemes, designed for stronger convergence and can be used at high-energies.

The post-Newtonian approximation

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Body Problem ◽  
Equations Of Motion ◽  
Two Body Problem ◽  
Newtonian Approximation ◽  
Actual Motion ◽  
Law Of Attraction ◽  
Universal Law ◽  
Two Bodies

This chapter embarks on a study of the two-body problem in general relativity. In other words, it seeks to describe the motion of two compact, self-gravitating bodies which are far-separated and moving slowly. It limits the discussion to corrections proportional to v2 ~ m/R, the so-called post-Newtonian or 1PN corrections to Newton’s universal law of attraction. The chapter first examines the gravitational field, that is, the metric, created by the two bodies. It then derives the equations of motion, and finally the actual motion, that is, the post-Keplerian trajectories, which generalize the post-Keplerian geodesics obtained earlier in the chapter.

The two-body problem: an effective-one-body approach

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Body Problem ◽  
Equations Of Motion ◽  
Reaction Force ◽  
Kerr Black Hole ◽  
Radiation Reaction ◽  
Spherically Symmetric ◽  
Geodesic Motion ◽  
Two Body Problem ◽  
Symmetric Spacetime ◽  
Radiation Reaction Force

This chapter presents the basics of the ‘effective-one-body’ approach to the two-body problem in general relativity. It also shows that the 2PN equations of motion can be mapped. This can be done by means of an appropriate canonical transformation, to a geodesic motion in a static, spherically symmetric spacetime, thus considerably simplifying the dynamics. Then, including the 2.5PN radiation reaction force in the (resummed) equations of motion, this chapter provides the waveform during the inspiral, merger, and ringdown phases of the coalescence of two non-spinning black holes into a final Kerr black hole. The chapter also comments on the current developments of this approach, which is instrumental in building the libraries of waveform templates that are needed to analyze the data collected by the current gravitational wave detectors.

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