scholarly journals Solutions of the Relativistic Two-Body Problem. I. Classical Mechanics

1972 ◽  
Vol 25 (2) ◽  
pp. 117 ◽  
Author(s):  
JL Cook
Keyword(s):  
Body Problem ◽  
Proper Time ◽  
Classical Mechanics ◽  
Hamiltonian Formalism ◽  
Calibration Method ◽  
Planetary Motion ◽  
Two Body Problem ◽  
Relativistic Harmonic Oscillator ◽  
Time Calibration ◽  
Relativistic Coulomb

The chief difficulty of lack of simultaneity of events in all Lorentz frames in relativistic mechanics is overcome using a proper time calibration method. The electromagnetic and gravitational point source interactions are derived. A Lagrangian and Hamiltonian formalism is shown to be valid. The mechanics can be quantized easily. Relativistic corrections are applied to the problem of planetary motion, a model for the relativistic Coulomb interaction is explored, and the relativistic harmonic oscillator is evaluated.

scholarly journals Entropy theorems in classical mechanics, general relativity, and the gravitational two-body problem

2016 ◽  
Vol 94 (6) ◽  
Author(s):  
Marius Oltean ◽  
Luca Bonetti ◽  
Alessandro D. A. M. Spallicci ◽  
Carlos F. Sopuerta
Keyword(s):  
General Relativity ◽  
Body Problem ◽  
Classical Mechanics ◽  
Two Body Problem

scholarly journals A Study about the Integration of the Elliptical Orbital Motion Based on a Special One-Parametric Family of Anomalies

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
José Antonio López Ortí ◽  
Francisco José Marco Castillo ◽  
María José Martínez Usó
Keyword(s):  
Linear Combination ◽  
Numerical Integration ◽  
Body Problem ◽  
Numerical Solutions ◽  
Orbital Motion ◽  
Planetary Motion ◽  
Two Body Problem ◽  
New Family ◽  
Analytical Development ◽  
Convex Linear Combination

This paper aimed to address the study of a new family of anomalies, called natural anomalies, defined as a one-parameter convex linear combination of the true and secondary anomalies, measured from the primary and the secondary focus of the ellipse, and its use in the study of analytical and numerical solutions of perturbed two-body problem. We take two approaches: first, the study of the analytical development of the basic quantities of the two-body problem to be used in the analytical theories of the planetary motion and second, the study of the minimization of the errors in the numerical integration by an appropriate choice of parameters in our family for each value of the eccentricity. The use of an appropriate value of the parameter can improve the length of the developments in the analytical theories and reduce the errors in the case of the numerical integration.

scholarly journals FOKKER-TYPE CONFINEMENT MODELS FROM EFFECTIVE LAGRANGIAN IN CLASSICAL YANG–MILLS THEORY

1999 ◽  
Vol 14 (28) ◽  
pp. 4519-4547 ◽  
Author(s):  
A. DUVIRYAK
Keyword(s):  
Body Problem ◽  
Particle System ◽  
Hamiltonian Formalism ◽  
Yang Mills ◽  
Moving Sources ◽  
Asymmetric Model ◽  
Two Body Problem ◽  
Regge Trajectories ◽  
Effective Lagrangian ◽  
Mills Field

Abelian potentials of pointlike moving sources are obtained from the nonstandard theory of Yang–Mills field. They are used for the construction of the time-symmetric and time-asymmetric Fokker-type action integrals describing the dynamics of two-particle system with confinement interaction. The time-asymmetric model is reformulated in the framework of the Hamiltonian formalism. The corresponding two-body problem is reduced to quadratures. The behavior of Regge trajectories is estimated within the semiclassical consideration.

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.

A Fitted Runge-Kutta-Nyström Method with Six Stages for the Integration of the Two-Body Problem

2011 ◽  
Author(s):  
A. A. Kosti ◽  
Z. A. Anastassi ◽  
T. E. Simos ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
...  
Keyword(s):  
Body Problem ◽  
Two Body Problem ◽  
Runge Kutta
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