A note on Earth's rotation angular velocity in the general-relativity framework

2001 ◽  
Vol 75 (12) ◽  
pp. 673-676 ◽  
Author(s):  
V. A. Brumberg ◽  
E. Groten
Keyword(s):  
General Relativity ◽  
Angular Velocity ◽  
Earth’S Rotation ◽  
Earth's Rotation

Zonal and tesseral harmonic perturbations of an artificial satellite

1966 ◽  
Vol 25 ◽  
pp. 323-325 ◽  
Author(s):  
B. Garfinkel
Keyword(s):  
Angular Velocity ◽  
Spherical Harmonics ◽  
Artificial Satellite ◽  
Compact Form ◽  
Earth’S Rotation ◽  
Earth's Rotation ◽  
Secular Variations ◽  
Tesseral Harmonics

The paper extends the known solution of the Main Problem to include the effects of the higher spherical harmonics of the geopotential. The von Zeipel method is used to calculate the secular variations of orderJmand the long-periodic variations of ordersJm/J2andnJm,λ/ω. HereJmandJm,λare the coefficients of the zonal and the tesseral harmonics respectively, withJm,0=Jm, andωis the angular velocity of the Earth's rotation. With the aid of the theory of spherical harmonics the results are expressed in a most compact form.

scholarly journals IV. On the dynamical theory of the tides of long period

1887 ◽  
Vol 41 (246-250) ◽  
pp. 337-342 ◽  
Keyword(s):  
Angular Velocity ◽  
Dynamical Theory ◽  
Equilibrium Theory ◽  
Earth’S Rotation ◽  
Laplace’S Method ◽  
Earth's Rotation ◽  
Long Period ◽  
Laplace's Method ◽  
William Thomson

In the following note an objection is raised against Laplace’s method of treating these tides, and a dynamical solution of the problem, founded on a paper by Sir William Thomson, is offered. Let θ , Φ be the colatitude and longitude of a point in the ocean, let ξ and η sin θ be the displacements from its mean position of the water occupying that point at the time t , let h be the height of the tide, and let ℓ be the height of the tide according to the equilibrium theory; let n be the angular velocity of the earth’s rotation, g gravity, a the earth’s radius, and γ the depth of the ocean at the point θ , Φ .

scholarly journals The relationship between global volcanic activity and variations in the velocity of Earth's rotation

2019 ◽  
Vol 484 (6) ◽  
pp. 729-733
Author(s):  
B. W. Levin ◽  
E. V. Sasorova ◽  
V. B. Gurianov ◽  
V. V. Yarmolyuk
Keyword(s):  
United States ◽  
Angular Velocity ◽  
Volcanic Activity ◽  
Rotational Velocity ◽  
Earth’S Rotation ◽  
Earth's Rotation ◽  
Deceleration Phase ◽  
The Earth ◽  
Smithsonian Institute ◽  
The Relationship

Analysis of observations of the Earth's rotational velocity and volcanic activity of the planet from 1720 until 2015 suggests that higher volcanic activity temporally coincided with periods of decreased angular velocity of Earth's rotation (deceleration), and, vice versa, lower volcanic activity coincided with the periods of increased velocity of the Earth's rotation (acceleration). Our analysis employed the data from the catalog by the Smithsonian Institute, United States, in which each volcanic explosion had its own determined value of the Volcanic Explosivity Index (VEI). The total number of selected intensive eruptions with VEI > 4 was 160, including 25 eruptions with VEI > 5. At present (beginning from 2006), the Earth was entry in a deceleration phase and series of catastrophic eruptions reveals the tendency toward intensifying volcanic activity.

Effect of the Change in the Geomagnetic Dipole Moment on the Rate of the Earth's Rotation

1972 ◽  
Vol 48 ◽  
pp. 229-230
Author(s):  
Takesi Yukutake
Keyword(s):  
Dipole Moment ◽  
Angular Velocity ◽  
Electromagnetic Coupling ◽  
Dipole Field ◽  
Earth’S Rotation ◽  
Present Moment ◽  
Earth’S Core ◽  
Earth's Rotation ◽  
Earth's Core ◽  
Geomagnetic Dipole

The electromagnetic coupling between the Earth's core and the mantle is studied when the geomagnetic dipole field varies periodically. The oscillation of the geomagnetic dipole moment with a period of 8000 years, its amplitude being 50% of the present moment, is capable of causing a fluctuation of 10−11 rad/s in the angular velocity of the mantle. The angular velocity increases with a decrease in the dipole moment.

scholarly journals Relationship between Seismic Activity and Variations in the Earth’s Rotation Angular Velocity

2018 ◽  
Vol 10 (2) ◽  
pp. 43 ◽  
Author(s):  
Elena Sasorova ◽  
Boris Levin
Keyword(s):  
Angular Velocity ◽  
Seismic Activity ◽  
Low Frequency ◽  
Rotation Velocity ◽  
Seismic Events ◽  
Earth’S Rotation ◽  
Earth's Rotation ◽  
The Earth ◽  
Frequency Components ◽  
New Phase

The Earth's seismic activity (SA) demonstrates a distinct unevenness both in space and in time. The periods of intensification of seismic activity are followed by periods of its decline. In this work, an attempt was first made to determine the effect of low-frequency components of the variations in the angular velocity of the Earth's rotation (AVER) on the dynamics of its seismic activity (for 1720 – 2017). Analysis of the time series of the density of seismic events and variations in the Earth's rotation velocity of about 300 years shows that each stage of reducing the angular velocity of rotation (braking) is accompanied by an increase in the density of seismic events, and the stages of increasing the angular velocity of rotation (acceleration) are accompanied by a decrease in the density of events. At present, the Earth is entering a new phase of deceleration (since 2005), which in recent years has already led to an increase in the global seismic activity.

A New Method of Integrating the Equations of Autonomous Strapdown INS

2018 ◽  
Vol 19 (10) ◽  
pp. 658-663
Author(s):  
Ya. G. Sapunkov ◽  
Yu. N. Chelnokov ◽  
A. V. Molodenkov
Keyword(s):  
Angular Velocity ◽  
Relative Velocity ◽  
Euler Method ◽  
Time Interval ◽  
Earth’S Rotation ◽  
Earth's Rotation ◽  
Rightmost Point ◽  
Cauchy Method ◽  
Orientation Quaternion ◽  
Object Relative

 We propose the new version of separating the process of integrating the differential equations, which describe the functioning of the strapdown inertial navigation system (SINS) in the normal geographic coordinate system (NGCS), into rapid and slow cycles. In this version, the vector of the relative velocity of an object is represented as a sum of a rapidly changing component and a slowly changing component. The equation for the rapidly changing component of the relative velocity includes the vectors of angular velocities of the Earth’s rotation, NGCS rotation, and, at the same time, the vectors of the apparent acceleration and gravity acceleration, because these accelerations partially balance each other, and at rest relative to the Earth are balanced completely. The equation of the slowly changing component of the relative velocity includes only the vector of angular velocity of the Earth’s rotation and the vector of NGCS rotation. The quaternion orientation of an object relative to the NGCS is represented as a product of two quaternions: a rapidly changing one, which is determined by the absolute angular velocity of an object, and slowly changing one, which is determined by the angular velocity of the NGCS. The right parts of the equations for each group of variables depend on the rapidly changing and slowly changing variables. In order to enable the independent integration of the slow and rapid cycle equations, the algorithm have been developed for integrating the equations using the predictor and corrector for the cases of instantaneous and integral information generated by SINS sensors. At each predictor step the Euler method is used to estimate the longitude, latitude and altitude of an object, slowly changing component of the relative velocity, and slowly changing multiplier of the orientation quaternion at the rightmost point of the slow cycle. Then the Euler-Cauchy method is used to integrate the equations for the rapidly changing components on the rapid cycle intervals, which are present in the slow cycle. The necessary values of the slowly changing components in the intermediate points are calculated using the formulas of linear interpolation. After the rapidly changing components are estimated at the rightmost point of the slow cycle, at the corrector step the Euler-Cauchy method is used to refine the values of the slowly changing components at the rightmost point of the slow cycle. Note that at the beginning of each slow cycle step the slowly changing component of velocity is equal to the value of the relative velocity of an object, and the rapidly changing component is zero. Similarly, at the beginning of each slow cycle step the slowly changing multiplier of object’s orientation quaternion equals to the quaternion of orientation of an object relative to the NGCS, and the rapidly changing multiplier of the orientation of an object has its scalar part equal to one, and its vector part equal to zero (this formula is derived from the quaternion formula for adding the finite rotations). SINS on a stationary base had been simulated in the presence of perturbations for a large time interval for a diving object, which drastically changes its height over short time periods. 

Long-term variations in the angular velocity of Earth’s rotation

2005 ◽  
Vol 50 (2) ◽  
pp. 95-99
Author(s):  
G. G. Denisov ◽  
V. V. Novikov ◽  
A. E. Fedorov
Keyword(s):  
Angular Velocity ◽  
Earth’S Rotation ◽  
Earth's Rotation ◽  
Long Term Variations
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