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The prolate spheroid is generated by rotation about the z-axis of an ellipse with semi-major axis c and semi-minor axis a; therefore, e may again be identified as the eccentricity. (See ellipse.) [3] These formulas are identical in the sense that the formula for S oblate can
The three coordinate surfaces of prolate spheroidal coordinates. The red prolate spheroid (stretched sphere) corresponds to μ = 1, and the blue two-sheet hyperboloid corresponds to ν = 45°. The yellow half-plane corresponds to φ = −60°, which is measured relative to the x-axis (highlighted in green).
This equation reduces to that of the volume of a sphere when all three elliptic radii are equal, and to that of an oblate or prolate spheroid when two of them are equal. The volume of an ellipsoid is 2 / 3 the volume of a circumscribed elliptic cylinder, and π / 6 the volume of the circumscribed box.
The unusual cosmic abundance of alpha nuclides has inspired geometric arrangements of alpha particles as a solution to nuclear shapes, although the atomic nucleus generally assumes a prolate spheroid shape. Nuclides can also be discus-shaped (oblate deformation), triaxial (a combination of oblate and prolate deformation) or pear-shaped. [7] [8]
The frictional coefficient of an arbitrary spheroid of volume equals = where is the translational friction coefficient of a sphere of equivalent volume (Stokes' law) = = (/)
Prolate spheroidal wave functions whose domain is a (portion of) the surface of the unit sphere are more generally called "Slepian functions". [9] These are of great utility in disciplines such as geodesy, [10] cosmology, [11] or tomography [12]
From ancient history to the modern day, the clitoris has been discredited, dismissed and deleted -- and women's pleasure has often been left out of the conversation entirely. Now, an underground art movement led by artist Sophia Wallace is emerging across the globe to challenge the lies, question the myths and rewrite the rules around sex and the female body.
The motion is simplified in the case of an axisymmetric body, in which the moment of inertia is the same about two of the principal axes. These cases include rotation of a prolate spheroid (the shape of an American football), or rotation of an oblate spheroid (the shape of a flattened sphere). In this case, the angular velocity describes a cone ...