Cylindrical Coordinates


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Related to Cylindrical Coordinates: Spherical coordinates

cylindrical coordinates

[sə′lin·drə·kəl ‚kō′ȯrd·ən·əts]
(mathematics)
A system of curvilinear coordinates in which the position of a point in space is determined by its perpendicular distance from a given line, its distance from a selected reference plane perpendicular to this line, and its angular distance from a selected reference line when projected onto this plane.

Cylindrical Coordinates

 

The cylindrical coordinates of a point M are the three numbers r, θ, and z characterizing the position of M in space (see Figure 1). The coordinates are called cylindrical because the coordinate surface r = const is a cylinder

Figure 1

whose elements are parallel to the z-axis. The relation between the cylindrical coordinates and the rectangular coordinates x, y, and z of M is given by the equations x = r cos θ, y = r sin θ, and z = z.

References in periodicals archive ?
The rectangular and the bipolar cylindrical coordinates are related by (13), (22):
A 3D cylindrical thin muffler was also studied by the FEM in order to verify the revised point source model used in the cylindrical coordinates.
For the heat transfer in isotropic material at axisymmetric conditions, it takes in cylindrical coordinates the following form
Displacement in x-direction is proportional to the cosine of the angle in cylindrical coordinate, and in y direction by sine of the angle.
l]bd[phi]'d[tau]'/(2[pi]), whose cylindrical coordinates are r' = [r.
p]) has to be winded onto a cylinder with the cylindrical coordinates ([[phi].
It is assumed, further, that the primary field is a monochromatic plane wave, p- or spolarized with respect to the xz-plane and incident upon the screen in a given angular direction [alpha], As the optical field so defined must be independent of y it will be convenient to use cylindrical coordinates (r, [phi], y) given by
Models of flow in twin screw extruders and internal mixers using cylindrical coordinates have been developed by various investigations (17-22) in recent years.
The geometry of a pancake sample in cylindrical coordinates is shown in Fig.
i] in cylindrical coordinates and the temperature at this intersection is given by [T.