Oblate spheroidal coordinates
Oblate spheroidal coordinates are a three-dimensional orthogonal coordinate system that results from rotating the two-dimensional elliptic coordinate system about the non-focal axis of the ellipse, i.e., the symmetry axis that separates the foci. Thus, the two foci are transformed into a ring of radius formula_1 in the "x"-"y" plane. (Rotation about the other axis produces prolate spheroidal coordinates.) Oblate spheroidal coordinates can also be considered as a limiting case of ellipsoidal coordinates in which the two largest semi-axes are equal in length.

Oblate spheroidal coordinates are often useful in solving partial differential equations when the boundary conditions are defined on an oblate spheroid or a hyperboloid of revolution. For example, they played an important role in the calculation of the Perrin friction factors, which contributed to the awarding of the 1926 Nobel Prize in Physics to Jean Baptiste Perrin. These friction factors determine the rotational diffusion of molecules, which affects the feasibility of many techniques such as protein NMR and from which the hydrodynamic volume and shape of molecules can be inferred. Oblate spheroidal coordinates are also useful in problems of electromagnetism (e.g., dielectric constant of charged oblate molecules), acoustics (e.g., scattering of sound through a circular hole), fluid dynamics (e.g., the flow of water through a firehose nozzle) and the diffusion of materials and heat (e.g., cooling of a red-hot coin in a water bath)
Q2588831
orthogonal
Concept
Q11210
coordinate system
Concept
Q1332432
elliptic coordinate system
DIS
Q7249552
prolate spheroidal coordinates
Concept
Q17123612
limiting case
UNK
Q1332363
ellipsoidal coordinates
Concept
Q21143897
semi-axes
UNK
Q271977
partial differential equation
Concept
Q208395
oblate spheroid
Concept
Q505628
hyperboloid of revolution
Concept
Q5837426
Perrin friction factors
UNK
Q38104
Nobel Prize in Physics
MEDIA
Q134085
Jean Baptiste Perrin
PER
Q4127028
rotational diffusion
UNK
Q864267
protein NMR
Concept
Q11075615
Oblate spheroidal coordinates
Concept
Q11075615
Oblate spheroidal coordinates
Concept
Q11075615
Oblate spheroidal coordinates
Concept
Q11075615
Oblate spheroidal coordinates
Concept
1926-01-01T00:00:00Z^^http://www.w3.org/2001/XMLSchema#dateTime
1926
DATE
+1^^http://www.w3.org/2001/XMLSchema#decimal
1
NUMBER
subclass of
subclass of
subclass of
award received