Due to the circular geometry of \ Omega, it will be convenient to use cylindrical coordinates, ( r, \ theta, z ).
22.
*PM : Laplace equation in cylindrical coordinates, id = 8555 new !-- WP guess : Laplace equation in cylindrical coordinates-- Status:
23.
*PM : Laplace equation in cylindrical coordinates, id = 8555 new !-- WP guess : Laplace equation in cylindrical coordinates-- Status:
24.
It is particularly helpful to write the displacement in cylindrical coordinates for a point force F _ z \, \ ! directed along the z-axis.
25.
This lies on the surface of the torus given by ( r-2 ) ^ 2 + z ^ 2 = 1 ( in cylindrical coordinates ).
26.
The three-dimensional wave equation, when expressed in elliptic cylindrical coordinates, may be solved by separation of variables, leading to the Mathieu differential equations.
27.
Since all of the surfaces of constant ?, ? and " z " are conicoid, Laplace's equation is separable in cylindrical coordinates.
28.
There are then Cartesian ( X, Y, Z ), spherical coordinates, and cylindrical coordinates that can be used, based on those 3 reference points.
29.
Other popular methods of describing the location of a point in three-dimensional space include cylindrical coordinates and spherical coordinates, though there are an infinite number of possible methods.
30.
Where the A _ n ( k ) are constants with respect to the cylindrical coordinates and the limits of the summation and integration are determined by the boundary conditions of the problem.
