applied mathematics, oblate spheroidal wave functions (like also prolate spheroidal wave functions and other related functions) are involved in the solution...

rotated around its long axis, “cigar shape“). Related are the oblate spheroidal wave functions (“pancake shaped” ellipsoid). Solve the Helmholtz equation...

called oblate spheroidal wave functions if oblate spheroidal coordinates are used and prolate spheroidal wave functions if prolate spheroidal coordinates...

Ellipsoidal dome Equatorial bulge Great ellipse Lentoid Oblate spheroidal coordinates Ovoid Prolate spheroidal coordinates Rotation of axes Translation of axes...

periodic differential equations, as for Lamé functions and prolate and oblate spheroidal wave functions. Mathieu's differential equations appear in a...

corresponding calculations for Mathieu functions, and oblate spheroidal wave functions and prolate spheroidal wave functions). With the following boundary conditions...

corresponding results for Mathieu functions, Lamé functions, prolate spheroidal wave functions, oblate spheroidal wave functions and others). In field theory...

A Maclaurin spheroid is an oblate spheroid which arises when a self-gravitating fluid body of uniform density rotates with a constant angular velocity...

prolate spheroid touching the sphere at the poles, with an equatorial radius (extraordinary index) equal to the polar radius of the oblate spheroidal index...

two-sheeted, consisting of a sphere (for the ordinary wave) and an oblate spheroid (for the extraordinary wave) touching each other at opposite points of a common...

solution for particles moving in the gravitational fields of prolate and oblate spheroids. This problem is named after Leonhard Euler, who discussed it in memoirs...

In a first approximation, the shape can be considered similar to oblate spheroids, with a semiaxis ratio of 2 to 8. This approximation can be used to...

rotating about an axis, the free surface will take the shape of an oblate spheroid: the approximate shape of the Earth due to its equatorial bulge. In...

generally assumes a prolate spheroid shape. Nuclides can also be discus-shaped (oblate deformation), triaxial (a combination of oblate and prolate deformation)...

describe horns with low acoustic loading, such as conic, quadratic, oblate spheroidal or elliptic cylindrical horns. These are designed more to control...

coordinates ⁠ r , θ , ϕ {\displaystyle r,\theta ,\phi } ⁠ are standard oblate spheroidal coordinates, which are equivalent to the cartesian coordinates where...

For example, the oblateness of a sphere of freely flowing material is often explained in terms of centrifugal force. The oblate spheroid shape reflects...

on Boyle's law) of the speed of sound in air, inferred the oblateness of Earth's spheroidal figure, accounted for the precession of the equinoxes as a...

motion is called Euler's free nutation. For a rigid Earth which is an oblate spheroid to a good approximation, the figure axis F would be its geometric axis...

Mathieu equation (best example), Lamé and ellipsoidal wave equations, oblate and prolate spheroidal wave equations, and equations with anharmonic potentials...

Johannes; Osten, Wolfgang (20 July 2017). "Measuring aspheres quickly: tilted wave interferometry". Optical Engineering. 56 (11): 111713. doi:10.1117/1.OE.56...

is slightly flatter at the poles while bulging at the Equator: an oblate spheroid. There are consequently slight deviations in the magnitude of gravity...

parallel to the geoid. Earth's gravitational field is not uniform. An oblate spheroid is typically used as the idealized Earth, but even if the Earth were...

orbits, such as the perturbations due to other bodies, or the impact of spheroidal rather than spherical bodies. Joseph-Louis Lagrange developed a new approach...

dielectrophoretic behavior of particles such as red blood cells (as oblate spheroids) or long thin tubes (as prolate ellipsoids) allowing the approximation...

underground aquifers, irrigate the surface naturally or via man-made wells. oblate spheroid The approximate geometric shape of the Earth: a three-dimensional ellipsoid...

to the axis of rotation. The Earth is not a perfect sphere but an oblate spheroid, with an equatorial diameter about 43 kilometers larger than its polar...

Earth, i.e. the arithmetic mean position of all points within the oblate spheroid that is the precise shape of the Earth. geocentric With reference to...

same principles. His prediction that the Earth should be shaped as an oblate spheroid was later vindicated by other scientists. His laws of motion were to...

varying geometric shape; spheres, discs, ellipsoids and prolate or oblate spheroids, and would be either isolated or set in a repeating pattern as part...