In a conservative model ( that is, without dissipations and acoustic irradiations and therefore in vacuum ), the oscillation modes of a membrane of radius a have the form in cylindrical coordinates
32.
:Similarly, spherical coordinates and cylindrical coordinates are alternative ways to describe the position of objects in 3D, and tend to be more convenient when dealing with spheres or cylinders, respectively.
33.
The journal sent their manuscript to be reviewed by Howard P . Robertson, who ( anonymously ) reported that the singularities in question were simply the harmless coordinate singularities of the employed cylindrical coordinates.
34.
In this cylindrical coordinate system, the incompressible flow can be described with a Stokes stream function " ? ", depending on " r " and " z ":
35.
The mathematical function which describes a Bessel beam is a solution of Bessel's differential equation, which itself arises from separable solutions to Laplace's equation and the Helmholtz equation in cylindrical coordinates.
36.
For instance, the coordinates for an hyperbolically accelerated reference frame are sometimes called Rindler coordinates, or those of a uniformly rotating reference frame are called rotating cylindrical coordinates ( or sometimes Born coordinates ).
37.
They are sometimes called " cylindrical polar coordinates " and " polar cylindrical coordinates ", and are sometimes used to specify the position of stars in a galaxy ( " galactocentric cylindrical polar coordinates " ).
38.
For the case of a sphere in a uniform far field flow, it is advantageous to use a cylindrical coordinate system ( " r ", ?, " z " ).
39.
The classic applications of parabolic cylindrical coordinates are in solving partial differential equations, e . g ., Laplace's equation or the Helmholtz equation, for which such coordinates allow a separation of variables.
40.
An elegant action-angle variables solution for the Kepler problem can be obtained by eliminating the redundant four-dimensional coordinates \ boldsymbol \ eta in favor of elliptic cylindrical coordinates ( ?, ?, ?)
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