oblate spheroidal coordinates造句

• "' Oblate spheroidal coordinates "'are a three-dimensional 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.
• An alternative and geometrically intuitive set of oblate spheroidal coordinates ( ?, ?, ? ) are sometimes used, where ? = cos ?.
• This two-fold degeneracy in the sign of " z " is evident from the equations transforming from oblate spheroidal coordinates to the Cartesian coordinates
• Figure 3 : Coordinate isosurfaces for a point P ( shown as a black sphere ) in the alternative oblate spheroidal coordinates ( ?, ?, ? ).
• Unlike the analogous oblate spheroidal coordinates, the prolate spheroid coordinates ( ?, ?, ? ) are " not " degenerate; in other words, there is a unique, reversible correspondence between them and the Cartesian coordinates
• In the non-relativistic limit where " M " ( or, equivalently, " r " " s " ) goes to zero, the Kerr metric becomes the orthogonal metric for the oblate spheroidal coordinates
• As is the case with spherical coordinates and spherical harmonics, Laplace's equation may be solved by the method of separation of variables to yield solutions in the form of "'oblate spheroidal harmonics "', which are convenient to use when boundary conditions are defined on a surface with a constant oblate spheroidal coordinate.
• As is the case with spherical coordinates, Laplaces equation may be solved by the method of separation of variables to yield solutions in the form of "'oblate spheroidal harmonics "', which are convenient to use when boundary conditions are defined on a surface with a constant oblate spheroidal coordinate ( See Smythe, 1968 ).
• 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)