Galerkin’s matrix for Neumann’s problem in the exterior of an oblate ellipsoid of revolution: gravity potential approximation by buried masses

2018 ◽  
Vol 63 (1) ◽  
pp. 1-34 ◽  
Author(s):  
Petr Holota ◽  
Otakar Nesvadba
Keyword(s):  
Gravity Potential ◽  
Potential Approximation ◽  
Oblate Ellipsoid ◽  
Ellipsoid Of Revolution

1. On the Figures of Equilibrium of a Rotating Mass of Fluid

1882 ◽  
Vol 11 ◽  
pp. 610-613 ◽  
Author(s):  
William Thomson
Keyword(s):  
Natural Philosophy ◽  
Oblate Ellipsoid ◽  
Single Ring ◽  
Figures Of Equilibrium ◽  
Ellipsoid Of Revolution ◽  
Definite Limit

(a) The oblate ellipsoid of revolution is proved in Thomson and Tait's Natural Philosophy (first edition, § 776, and the Table of § 772) to be stable, if the condition of being an ellipsoid of revolution be imposed. It is obviously not stable for very great eccentricities without this double condition of being both a figure of revolution and ellipsoidal.(b) If the condition of being a figure of revolution is imposed, without the condition of being an ellipsoid, there is, for large enough moment of momentum, an annular figure of equilibrium which is stable, and an ellipsoidal figure which is unstable. It is probable, that for moment of momentum greater than one definite limit and less than another, there is just one annular figure of equilibrium, consisting of a single ring.

scholarly journals Stokes constants of an oblate ellipsoid of revolution with equidensites homothetic to its surface

2017 ◽  
Vol 50 (3) ◽  
pp. 318-324 ◽  
Author(s):  
K. V. Kholshevnikov ◽  
D. V. Milanov ◽  
V. Sh. Shaidulin
Keyword(s):  
Oblate Ellipsoid ◽  
Ellipsoid Of Revolution

scholarly journals Solutions to the ellipsoidal Clairaut constant and the inverse geodetic problem by numerical integration

2012 ◽  
Vol 2 (3) ◽  
pp. 162-171 ◽  
Author(s):  
L. E. Sjöberg
Keyword(s):  
Fixed Points ◽  
Numerical Integration ◽  
Special Role ◽  
Oblate Ellipsoid ◽  
Ellipsoid Of Revolution ◽  
The Given ◽  
Special Case

AbstractWe derive computational formulas for determining the Clairaut constant, i.e. the cosine of the maximum latitude of the geodesic arc, from two given points on the oblate ellipsoid of revolution. In all cases the Clairaut constant is unique. The inverse geodetic problem on the ellipsoid is to determine the geodesic arc between and the azimuths of the arc at the given points. We present the solution for the fixed Clairaut constant. If the given points are not(nearly) antipodal, each azimuth and location of the geodesic is unique, while for the fixed points in the ”antipodal region”, roughly within 36”.2 from the antipode, there are two geodesics mirrored in the equator and with complementary azimuths at each point. In the special case with the given points located at the poles of the ellipsoid, all meridians are geodesics. The special role played by the Clairaut constant and the numerical integration make this method different from others available in the literature.

scholarly journals Stokes constants of an oblate ellipsoid of revolution with equidensites homothetic to its surface

2017 ◽  
Vol 4(62) (3) ◽  
pp. 516-524
Author(s):  
Konstantin V. Kholshevnikov ◽  
◽  
Danila V. Milanov ◽  
Vakhit Sh. Shaidulin ◽  
◽  
...  
Keyword(s):  
Oblate Ellipsoid ◽  
Ellipsoid Of Revolution

scholarly journals CONTRIBUTION OF DRIFT AND DIFFUSION TO WATER CAPACITY DEIONIZATION

2021 ◽  
pp. 162-165
Author(s):  
D.V. Kudin ◽  
V.M. Ostroushko ◽  
A.V. Pashchenko ◽  
S.V. Rodionov ◽  
M.O. Yegorov ◽  
...  
Keyword(s):  
Applied Voltage ◽  
Capacitive Deionization ◽  
Cavity Size ◽  
Water Capacity ◽  
Deep Cavity ◽  
Oblate Ellipsoid ◽  
Approximate Relationship ◽  
Ellipsoid Of Revolution ◽  
And Diffusion

Drift and diffusion of ions in a cavity having the shape of oblate ellipsoid of revolution are considered. The obtained approximate relationship, between the time of drift and diffusion filling of deep cavity with ions, contains the applied voltage and the ratio of cavity size to the distance between electrodes. It shows that in the performed experiments with the device for water capacitive deionization the filling of electrodes by ions was carried out, mainly, due to diffusion.

The General Term in the Expansion for Meridian Length

1971 ◽  
Vol 25 (2) ◽  
pp. 156-163
Author(s):  
Erwin Schmid
Keyword(s):  
General Term ◽  
Arc Length ◽  
Oblate Ellipsoid ◽  
Ellipsoid Of Revolution

The series for arc length of the meridian of an oblate ellipsoid of revolution is developed to the nth term in powers of e2 and of the sine and cosine of the geodetic latitude. This type of expansion seems to be more efficient for use in electronic computation than the traditional series in terms of multiple angles ofɸ. Inclusion of the general term allows any desired degree of precision and an estimate of the neglected portion of the function.

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