scholarly journals On the Problem of post-Newtonian Rotational Motion

1997 ◽  
Vol 165 ◽  
pp. 383-390
Author(s):  
Sergei A. Klioner
Keyword(s):  
General Relativity ◽  
Angular Velocity ◽  
Rotational Motion ◽  
Earth Rotation ◽  
Deformable Body ◽  
Gravitational Fields ◽  
The Earth ◽  
Newtonian Approximation ◽  
Deformable Bodies ◽  
Tensor Of Inertia

AbstractThe problems of modeling of the rotational motion of the Earth are considered in the framework of general relativity. Both, rigid and deformable bodies are discussed. Rigorous definitions of the tensor of inertia, Tisserand-like axes and the angular velocity of rotation of an extended deformable body moving and rotating in external gravitational fields are proposed in the first post-Newtonian approximation. The implications of these post-Newtonian definitions on modeling of Earth rotation are analyzed.

scholarly journals Tidal Variations of the Earth Rotation

2000 ◽  
Vol 178 ◽  
pp. 565-569
Author(s):  
J.M. Ferrándiz ◽  
Yu. V. Barkin ◽  
J. Getino
Keyword(s):  
Angular Velocity ◽  
Earth Rotation ◽  
Polar Motion ◽  
Deformable Body ◽  
The Moon ◽  
First Order ◽  
Andoyer Variables ◽  
The Earth ◽  
Tidal Deformations ◽  
Tidal Variations

AbstractThe equations for the rotation of a weakly deformable celestial body in non canonical Andoyer variables have been used to study the perturbation of Earth rotation due to tidal deformation raised by the Moon and Sun. A theory of the perturbed rotational motion of an isolated weakly deformable body in Andoyer variables and in components of the angular velocity has been developed. Mantle tidal deformations due to lunar and solar influences were analytically described and taken into account. Perturbations of the first order in the Earth’s polar motion were determined.

scholarly journals Angular velocity of rotation of extended bodies in general relativity

1996 ◽  
Vol 172 ◽  
pp. 309-320
Author(s):  
S.A. Klioner
Keyword(s):  
General Relativity ◽  
Angular Velocity ◽  
Rigid Body ◽  
Rotational Motion ◽  
The Body ◽  
Astronomical Observations ◽  
Newtonian Approximation ◽  
Accurate Definition ◽  
Principal Axes ◽  
Definition Of

We consider rotational motion of an arbitrarily composed and shaped, deformable weakly self-gravitating body being a member of a system of N arbitrarily composed and shaped, deformable weakly self-gravitating bodies in the post-Newtonian approximation of general relativity. Considering importance of the notion of angular velocity of the body (Earth, pulsar) for adequate modelling of modern astronomical observations, we are aimed at introducing a post-Newtonian-accurate definition of angular velocity. Not attempting to introduce a relativistic notion of rigid body (which is well known to be ill-defined even at the first post-Newtonian approximation) we consider bodies to be deformable and introduce the post-Newtonian generalizations of the Tisserand axes and the principal axes of inertia.

scholarly journals Relativistic Considerations for Precession and Nutation

1998 ◽  
Vol 11 (1) ◽  
pp. 173-176
Author(s):  
S.A. Klioner ◽  
M. Soffel
Keyword(s):  
General Relativity ◽  
Rotational Motion ◽  
Earth Rotation ◽  
Equations Of Motion ◽  
Relativistic Effects ◽  
Point Of View ◽  
Extended Body ◽  
The Earth ◽  
Celestial Bodies

Abstract The whole scope of problems related with the rotational motion of celestial bodies is briefly discussed. Relativistic modeling of the Earth rotation is considered from a conceptual point of view. Relativistic effects in rotational equations of motion of an extended body in general relativity are discussed. Numerical values of the effects are given.

A simplified technique for determining the rotational motion of a satellite based on the onboard measurements of the angular velocity and magnetic field of the Earth

2016 ◽  
Vol 54 (5) ◽  
pp. 375-387 ◽  
Author(s):  
V. I. Abrashkin ◽  
K. E. Voronov ◽  
I. V. Piyakov ◽  
Yu. Ya. Puzin ◽  
V. V. Sazonov ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Angular Velocity ◽  
Rotational Motion ◽  
The Earth

scholarly journals Geophysical models of the surface global vorticity vector

1988 ◽  
Vol 128 ◽  
pp. 411-411
Author(s):  
Erik W. Grafarend
Keyword(s):  
Spherical Harmonics ◽  
Earth Rotation ◽  
Polar Motion ◽  
Deformable Body ◽  
Earth Model ◽  
Order Zero ◽  
The Earth ◽  
Vorticity Vector ◽  
Ellipsoid Of Revolution ◽  
Length Of The Day

Within the framework of Newtonian kinematics the local vorticity vector is introduced and averaged with respect to global earth geometry, namely the ellipsoid of revolution. For a deformable body like the earth the global vorticity vector is defined as the earth rotation. A decomposition of the Lagrangean displacement and of the Lagrangean vorticity vector into vector spherical harmonics, namely into spheroidal and toroidal parts, proves that the global vorticity vector only contains toroidal coefficients of degree and order one (polar motion) and toroidal coefficients of degree one and order zero (length of the day) in the case of an ellipsoidal earth. Once we assume an earth model of type ellipsoid of revolution the earth rotation is also slightly dependent on the ellipsoidal flattening and the radial derivative of the spheroidal coefficients of degree two and order one.

scholarly journals Rers2014 and Mrs2014: New High-Precision Rigid Earth Rotation and Moon Rotation Series

2015 ◽  
Vol 50 (1) ◽  
pp. 35-40
Author(s):  
V.V. Pashkevich
Keyword(s):  
Numerical Solution ◽  
Numerical Investigation ◽  
High Precision ◽  
Rotational Motion ◽  
Earth Rotation ◽  
Euler Angles ◽  
Time Intervals ◽  
The Earth ◽  
Long Time ◽  
Rigid Earth

Abstract Numerical investigation of the Earth and Moon rotational motion dynamics is carried out at a long time intervals. In our previous studies (Pashkevich, 2013), (Pashkevich and Eroshkin, 2011) the high-precision Rigid Earth Rotation Series (designated RERS2013) and Moon Rotation Series (designated MRS2011) were constructed. RERS2013 are dynamically adequate to the JPL DE422/LE422 (Folkner, 2011) ephemeris over 2000 and 6000 years and include about 4113 periodical terms (without attempt to estimate new subdiurnal and diurnal periodical terms). MRS2011 are dynamically adequate to the JPL DE406/LE406 (Standish, 1998) ephemeris over 418, 2000 and 6000 years and include about 1520 periodical terms. In present research have been improved the Rigid Earth Rotation Series RERS2013 and Moon Rotation Series MRS2011, and as a result have been constructed the new high-precision Rigid Earth Rotation Series RERS2014 and Moon Rotation Series MRS2014 dynamically adequate to the JPL DE422/LE422 ephemeris over 2000 and 6000 years, respectively. The elaboration of RERS2013 is carried out by means recalculation of sub-diurnal and diurnal periodical terms. The residuals in Euler angles between the numerical solution and RERS2014 do not surpass 3 ìas over 2000 years. Improve the accuracy of the series MRS2011 is obtained by using the JPL DE422/LE422 ephemeris. The residuals in the perturbing terms of the physical librations between the numerical solution and MRS2014 do not surpass 8 arc seconds over 6000 years

A FUNDAMENTAL THEORY OF THE MAGNETISM OF MASSIVE ROTATING BODIES

1951 ◽  
Vol 29 (6) ◽  
pp. 470-479 ◽  
Author(s):  
George Luchak
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Rotational Motion ◽  
Phenomenological Theory ◽  
Variable Stars ◽  
Fundamental Theory ◽  
Gravitational Fields ◽  
The Earth ◽  
The Magnetic Field ◽  
Rotating Bodies

A phenomenological theory, based on a relativistically covariant generalization of Maxwell's equations to include gravitational fields, is developed to account for the magnetic fields of massive rotating bodies. The equations yield the Wilson–Blackett expression for the magnetic moment of the earth and stars but give no magnetic field for mass-bodies moving without rotation in their own gravitational fields. They indicate that the magnetic field due to the motion of the earth in its orbit is negligibly small compared to the field due to its rotational motion, and they provide a possible explanation for the variable magnetic fields of light-variable stars.

scholarly journals Relativity effects in the rotation of the Earth and the motion of atmospheric masses

1986 ◽  
Vol 114 ◽  
pp. 289-292
Author(s):  
V. G. Shkodrov ◽  
V. G. Ivanova
Keyword(s):  
Angular Velocity ◽  
Observational Data ◽  
Atmospheric Pressure ◽  
Earth Rotation ◽  
Numerical Results ◽  
Moment Of Inertia ◽  
The Earth ◽  
Rotation Of The Earth ◽  
The Moment

On the basis of observational data on atmospheric pressure (1963–1967), the variation of the moment of inertia, and, with certain restrictions, the changes in the angular velocity of the Earth are obtained. The numerical results derived are compared to the relativity effects in Earth rotation. The comparison shows that both effects are equal in periods and very close in amplitudes.

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