NationMaster - Encyclopedia: Cylindrical coordinate system

The cylindrical coordinate system is a three-dimensional coordinate system which essentially extends circular polar coordinates by adding a third coordinate (usually denoted $h$ ) which measures the height of a point above the plane. Image File history File links Example for a cylindrical coordinate system File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Image File history File links Example for a cylindrical coordinate system File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... In mathematics as applied to geometry, physics or engineering, a coordinate system is a system for assigning a tuple of numbers to each point in an n-dimensional space. ... A polar grid with several angles labeled in degrees In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by an angle and a distance. ...

A point P is given as $(r,θ, h)$ . In terms of the Cartesian coordinate system: Fig. ...

$r$ is the distance from O to P', the orthogonal projection of the point P onto the XY plane. This is the same as the distance of P to the z-axis.
$θ$ is the angle between the positive x-axis and the line OP', measured counterclockwise.
$h$ is the same as $z$ .
Thus, the conversion function $f$ from cylindrical coordinates to Cartesian coordinates is $f (x, y, z) = (r cosθ, r sinθ, h)$ .

For use in physical sciences and technology, the recommended international standard notation is ρ, φ, z (ISO 31-11). ISO 31-11 is the part of international standard ISO 31 that defines mathematical signs and symbols for use in physical sciences and technology. ...

Some mathematicians indeed use $(r,θ, z)$ .

Cylindrical coordinates are useful in analyzing surfaces that are symmetrical about an axis, with the z-axis chosen as the axis of symmetry. For example, the infinitely long circular cylinder that has the Cartesian equation x² + y² = c² has the very simple equation r = c in cylindrical coordinates. Hence the name "cylindrical" coordinates.

Line and volume elements

See multiple integral for details of volume integration in cylindrical coordinates, and Del in cylindrical and spherical coordinates for vector calculus formula.

In many problems involving cylindrical polar coordinates, it is useful to know the line and volume elements; these are used in integration to solve problems involving paths and volumes. To meet Wikipedias quality standards, this article or section may require cleanup. ... This is a list of some vector calculus formulae of general use in working with standard coordinate systems. ... Vector calculus (also called vector analysis) is a field of mathematics concerned with multivariate real analysis of vectors in two or more dimensions. ...

The line element is $dl = dr,mathbf{hat r} + r,dtheta,boldsymbol{hattheta} + dz,mathbf{hat z}$ . The line element in mathematics can most generally be thought of as the square of the change in a position vector in an affine space equated to the square of the change of the arc length. ...

The volume element is $dV = r,dr,dtheta,dz$ .

The gradient is $nabla = mathbf{hat r}frac{partial}{partial r} + boldsymbol{hat theta}frac{1}{r}frac{partial}{partial theta} + mathbf{hat z}frac{partial}{partial z}$ . For other uses, see Gradient (disambiguation). ...

Category: Coordinate systems This is a list of canonical coordinate transformations. ... Fig. ... A point plotted using the spherical coordinate system In mathematics, the spherical coordinate system is a coordinate system for representing geometric figures in three dimensions using three coordinates: the radial distance of a point from a fixed origin, the zenith angle from the positive z-axis, and the azimuth angle... Parabolic coordinates are an alternative system of coordinates for three dimensions. ... // Vector fields in cylindrical coordinates Vectors are defined in cylindrical coordinates by (Ï,Ï†,z), where Ï is the length of the vector projected onto the X-Y-plane, Ï† is the angle of the projected vector with the positive X-axis (0 â‰¤ Ï† < 2Ï€), z is the regular z-coordinate. ...

Results from FactBites:

Coordinate system - Wikipedia, the free encyclopedia (1155 words)
	Curvilinear coordinates are a generalization of coordinate systems generally; the system is based on the intersection of curves.
	Circular coordinate system (commonly referred to as the polar coordinate system) represents a point in space by an angle and a distance from the origin.
	Cylindrical coordinate system represents a point in space by an angle, a distance from the origin and a height.

Cylindrical coordinate system - Wikipedia, the free encyclopedia (277 words)
	The cylindrical coordinate system is a three-dimensional system which essentially extends circular polar coordinates by adding a third coordinate (usually denoted h) which measures the height of a point above the plane.
	Cylindrical coordinates are useful in analyzing surfaces that are symmetrical about an axis, with the z-axis chosen as the axis of symmetry.
	In many problems involving cylindrical polar coordinates, it is useful to know the line and volume elements; these are used in integration to solve problems involving paths and volumes.

More results at FactBites »

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Line and volume elements