Variation of the equatorial moments of inertia associated with a 6-year westward rotary motion in the Earth

2020 ◽  
Vol 542 ◽  
pp. 116316 ◽  
Author(s):  
B.F. Chao ◽  
Y. Yu
Keyword(s):  
Rotary Motion ◽  
Moments Of Inertia ◽  
The Earth

III. On Fessel's gyroscope

1856 ◽  
Vol 7 ◽  
pp. 43-48
Keyword(s):  
Royal Society ◽  
Rotary Motion ◽  
The Earth ◽  
Rotation Of The Earth ◽  
Mechanical Proof ◽  
Present Opportunity

Since the announcement of M. Foucault’s beautiful experiment which has afforded us a new mechanical proof of the rotation of the earth on its axis, the phenomena of rotary motion have received renewed attention, and many ingenious instruments have been contrived to exhibit and to explain them. One of the most instructive of these is the Gyroscope invented by M. Fessel of Cologne, described in its earlier form in Poggendorff’s Annalen for September 1853, and which, with some improvements by Prof. Plücker and some further modifications suggested by myself, I take the present opportunity of bringing before the Royal Society.

Thermal effects on the figure of the Moon

1967 ◽  
Vol 296 (1446) ◽  
pp. 266-269 ◽  
Keyword(s):  
Thermal Effects ◽  
Hydrostatic Equilibrium ◽  
Moment Of Inertia ◽  
The Moon ◽  
Moments Of Inertia ◽  
The Earth ◽  
Principal Moments Of Inertia ◽  
Long Time ◽  
The Stability ◽  
Lunar Rotation

Before discussing its cause, one must be clear in exactly what respect the lunar figure deviates from the equilibrium one. This is necessary because there has been confusion over the question for a long time. It was known early that the Moon’s ellipsoid of inertia is triaxial and that the differences of the principal moments of inertia determined from observations are several times larger than the theoretical values corresponding to hydrostatic equilibrium. The stability of lunar rotation requires that the axis of least moment of inertia point approximately towards the Earth and the laws of Cassini show that it is really so.

scholarly journals On the Equation of Precession and Nutation of the Dynamically Unbalanced Earth

1980 ◽  
Vol 78 ◽  
pp. 157-157
Author(s):  
Zh. S. Erzhanov ◽  
A. A. Kolybaev ◽  
Al. K. Egorov
Keyword(s):  
Approximate Solution ◽  
Moments Of Inertia ◽  
Rigorous Theory ◽  
The Earth ◽  
Rotation Of The Earth

In contrast to the deduction of the equations of precession and nutation adopted as a standard by the IAU, the authors develop a rigorous theory of the rotation of the Earth taking into account the inequality of the equatorial moments of inertia of the Earth and retaining small terms usually neglected to simplify an approximate solution.The equation is expressed in terms of the so-called Beletsky-Chernousko's variables used in astrodynamics.

Mass distribution and moments of inertia in the outer shells of the Earth

Terra Nova ◽  
2012 ◽  
Vol 25 (1) ◽  
pp. 38-47
Author(s):  
Michele Caputo ◽  
Riccardo Caputo
Keyword(s):  
Mass Distribution ◽  
Moments Of Inertia ◽  
The Earth

Equatorial flattening and principal moments of inertia of the earth

1984 ◽  
Vol 28 (1) ◽  
pp. 9-10 ◽  
Author(s):  
Milan Burša ◽  
Zdislav Šíma ◽  
M. Pick
Keyword(s):  
Moments Of Inertia ◽  
The Earth ◽  
Principal Moments Of Inertia

scholarly journals XV. A new theory of the rotary motion of bodies affected by forces disturbing such motion.

1777 ◽  
Vol 67 ◽  
pp. 266-295
Keyword(s):  
Rotary Motion ◽  
The Sun ◽  
The Earth ◽  
Rotatory Motion ◽  
Better Than

I am induced to consider this paper as not unworthy the notice of this Society, through a persuasion that the theory herein contained will conduce to the improvement of science, by enabling the reader to form a true idea, and accordingly to make a computation of the motion (or change) of the axis about which a body having a rotatory motion will turn, or have a tendency to turn, upon being affected by a force disturbing its rotation; particularly of the motion of the earth's axis arising from the attraction of the Sun and Moon on the protuberant matter of the earth above its greatest inscribed sphere: which compound motion, I conceive, has not been rightly explained by any one of the eminent mathematicians whose writings on the same subject have come to my hands. Whether in this essay I have really succeeded better than other writers who have attempted an explanation of such motion, I submit to gentlemen well versed in mechanics to determine.

scholarly journals IV. Notes on physical geology

1878 ◽  
Vol 26 (179-184) ◽  
pp. 51-63
Keyword(s):  
Moment Of Inertia ◽  
Total Moment ◽  
Moments Of Inertia ◽  
Axis Of Rotation ◽  
The Earth ◽  
Ellipsoid Of Revolution ◽  
Physical Geology

1. If the earth’s surface be an ellipsoid of revolution, whose moments of inertia round the polar and equatorial axes are C and A, and if μ be the mass of a mountain placed on any meridian, with coordinates z, x , it is required to find the change of position in the earth’s axis caused by the addition of the mass μ (supposed in the first instance to be placed upon the earth ab extra ). If λ be the latitude on which μ is placed, we have tan λ = z/w ; and if θ be the angle made with the earth’s axis by any axis x in the meridian of μ , if I be the total moment of inertia round this axis, we have I=A sin 2 θ +C cos 2 θ + μ ( x 2 cos 2 θ + z 2 sin 2 θ –2 xz sin θ cos θ ) . . . (1) The new axis of rotation is that which makes I = maximum, or d l = 0, from which we find, after some reduction, —tan 2 θ =2 μxz /(C–A)+μ( x 2 – z 2 . . . . (2) If we make θ = maximum, or dθ =0, we ascertain the position in which the mass μ must be placed so as to produce the maximum shift in the position of the earth’s axis.

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