scholarly journals Lense–Thirring precession and gravito–gyromagnetic ratio

2020 ◽  
Vol 80 (11) ◽  
Author(s):  
A. Stepanian ◽  
Sh. Khlghatyan ◽  
V. G. Gurzadyan
Keyword(s):  
Equations Of Motion ◽  
Relativistic Correction ◽  
Gyromagnetic Ratio ◽  
Relativistic Corrections

AbstractThe geodesics of bound spherical orbits i.e. of orbits performing Lense–Thirring precession, are obtained in the case of the $$\varLambda $$ Λ term within the gravito-electromagnetic formalism. It is shown that the presence of the $$\varLambda $$ Λ -term in the equations of gravity leads to both relativistic and non-relativistic corrections in the equations of motion. The contribution of the $$\varLambda $$ Λ -term in the Lense–Thirring precession is interpreted as an additional relativistic correction and the gravito–gyromagnetic ratio is defined.

NUMERICAL CALCULATIONS OF THE SMALL RELATIVISTIC CORRECTIONS OF ANISOTROPIC QUANTUM HARMONIC OSCILLATOR ENERGY EIGENVALUES: THE TWO- AND THREE-DIMENSIONAL CASE

1996 ◽  
Vol 07 (04) ◽  
pp. 563-571
Author(s):  
GHEORGHE ARDELEAN ◽  
ION I. COTĂESCU
Keyword(s):  
Harmonic Oscillator ◽  
Three Dimensional ◽  
Relativistic Correction ◽  
Numerical Calculations ◽  
Dimensional Case ◽  
Quantum Harmonic Oscillator ◽  
Energy Eigenvalues ◽  
Relativistic Corrections

In this paper the small relativistic correction for the energy eigenvalues of the two- and three-dimensional anisotropic quantum harmonic oscillator are calculated, using as eigenstates [Formula: see text], for different values of the relativistic parameters βi ≡ ħwi / m0c2 with i = 1, 2 and 3.

scholarly journals THE FORCE OF GRAVITY IN SCHWARZSCHILD AND GULLSTRAND–PAINLEVÉ COORDINATES

2009 ◽  
Vol 18 (14) ◽  
pp. 2289-2294 ◽  
Author(s):  
CARL BRANNEN
Keyword(s):  
Equations Of Motion ◽  
Relativistic Correction ◽  
First Order ◽  
Geodesic Equations ◽  
Affine Parameter ◽  
Tests Of Gravity

We derive the exact equations of motion (in Newtonian, F = ma, form) for test masses in Schwarzschild and Gullstrand–Painlevé coordinates. These equations of motion are simpler than the usual geodesic equations obtained from Christoffel tensors, in that the affine parameter is eliminated. The various terms can be compared against tests of gravity. In force form, gravity can be interpreted as resulting from a flux of superluminal particles (gravitons). We show that the first order relativistic correction to Newton's gravity results from a two-graviton interaction.

scholarly journals Equations of motion for isolated bodies with relativistic corrections including the radiation reaction force

1986 ◽  
Vol 114 ◽  
pp. 19-34 ◽  
Author(s):  
L. P. Grishchuk ◽  
S. M. Kopejkin
Keyword(s):  
Equations Of Motion ◽  
Reaction Force ◽  
Slow Motion ◽  
Major Axis ◽  
Radiation Reaction ◽  
Secular Change ◽  
Semi Major Axis ◽  
Relativistic Corrections ◽  
Relativistic Mass ◽  
Osculating Elements

We have derived in an explicit form the equations of motion for two spherically-symmetric non rotating bodies in the slow motion approximation. The equations include relativistic corrections of order (v/c)2, (v/c)4 and (v/c)5 to the newtonian equations of motion. It is shown that the equations depend on the only parameter characterizing each body, namely on its relativistic mass, regardless of its internal structure and degree of compactness. This means that the equations can also be applied to bodies with a strong internal gravity, such as neutron stars and black holes. It is shown that in the (v/c)2 and (v/c)4 approximations the equations can be derived from a Lagrangian. The Lagrangian is given in an exact form. The integration of the equations of motion is performed by the method of osculating elements. The formulae for secular change of the semi-major axis and eccentricity coincide precisely with the standard ones whose derivation is based on a calculation of the energy flux in the outgoing gravitational waves.

scholarly journals A relativistic motion integrator: numerical accuracy and illustration with BepiColombo and Mars-NEXT

2009 ◽  
Vol 5 (S261) ◽  
pp. 144-146 ◽  
Author(s):  
A. Hees ◽  
S. Pireaux
Keyword(s):  
Numerical Study ◽  
Equations Of Motion ◽  
Relativistic Motion ◽  
Numerical Accuracy ◽  
Relativistic Corrections ◽  
Relativistic Equations

AbstractToday, the motion of spacecraft is still described by the classical Newtonian equations of motion plus some relativistic corrections. This approach might become cumbersome due to the increasing precision required. We use the Relativistic Motion Integrator (RMI) approach to numerically integrate the native relativistic equations of motion for a spacecraft. The principle of RMI is presented. We compare the results obtained with the RMI method with those from the usual Newton plus correction approach for the orbit of the BepiColombo (around Mercury) and Mars-NEXT (around Mars) orbiters. Finally, we present a numerical study of RMI and we show that the RMI approach is relevant to study the orbit of spacecraft.

NUMERICAL CALCULATIONS OF THE SMALL RELATIVISTIC CORRECTIONS OF QUANTUM HARMONIC OSCILLATOR ENERGY EIGENVALUES

1996 ◽  
Vol 06 (06) ◽  
pp. 773-780
Author(s):  
GHEORGHE ARDELEAN
Keyword(s):  
Harmonic Oscillator ◽  
Relativistic Correction ◽  
Numerical Calculations ◽  
Quantum Harmonic Oscillator ◽  
Energy Eigenvalues ◽  
Relativistic Corrections ◽  
Relativistic Parameter

The relativistic correction of the energy eigenvalues of quantum harmonic oscillator (QHO) are calculated using [Formula: see text] as eigenstates, for different values of the relativistic parameter α ≡ ħω/m0c2.

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

On the motion of comet P/d’Arrest

1974 ◽  
Vol 22 ◽  
pp. 145-148
Author(s):  
W. J. Klepczynski
Keyword(s):  
Equations Of Motion ◽  
Variational Equations ◽  
Partial Derivatives

AbstractThe differences between numerically approximated partial derivatives and partial derivatives obtained by integrating the variational equations are computed for Comet P/d’Arrest. The effect of errors in the IAU adopted system of masses, normally used in the integration of the equations of motion of comets of this type, is investigated. It is concluded that the resulting effects are negligible when compared with the observed discrepancies in the motion of this comet.

Validation of a Belt Model for Prediction of Hub Forces from a Rolling Tire4

2009 ◽  
Vol 37 (2) ◽  
pp. 62-102 ◽  
Author(s):  
C. Lecomte ◽  
W. R. Graham ◽  
D. J. O’Boy
Keyword(s):  
Internal Pressure ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Prediction Method ◽  
Analytical Models ◽  
Beam Model ◽  
Impedance Boundary ◽  
Bending Waves ◽  
Tire Rotation ◽  
Three Dimensional Models

Abstract An integrated model is under development which will be able to predict the interior noise due to the vibrations of a rolling tire structurally transmitted to the hub of a vehicle. Here, the tire belt model used as part of this prediction method is first briefly presented and discussed, and it is then compared to other models available in the literature. This component will be linked to the tread blocks through normal and tangential forces and to the sidewalls through impedance boundary conditions. The tire belt is modeled as an orthotropic cylindrical ring of negligible thickness with rotational effects, internal pressure, and prestresses included. The associated equations of motion are derived by a variational approach and are investigated for both unforced and forced motions. The model supports extensional and bending waves, which are believed to be the important features to correctly predict the hub forces in the midfrequency (50–500 Hz) range of interest. The predicted waves and forced responses of a benchmark structure are compared to the predictions of several alternative analytical models: two three dimensional models that can support multiple isotropic layers, one of these models include curvature and the other one is flat; a one-dimensional beam model which does not consider axial variations; and several shell models. Finally, the effects of internal pressure, prestress, curvature, and tire rotation on free waves are discussed.

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