toroidal coordinates
1Toroidal coordinates — are a three dimensional orthogonal coordinate system that results from rotating the two dimensional bipolar coordinate system about the axis that separates its two foci. Thus, the two foci F {1} and F {2} in bipolar coordinates become a ring of… …
2Toroidal — may refer to:*Toroidal inductors and transformers, a type of electrical device *Toroid, a doughnut shaped object whose surface is a torus *Toroidal and poloidal, directions in magnetohydrodynamics *Toroidal coordinates, a three dimensional… …
3Toroidal and poloidal — The earliest use of these terms cited by the Oxford English Dictionary (OED) is by Walter M. Elsasser (1946) in the context of the generation of the Earth s magnetic field by currents in the core, with toroidal being in the same direction as… …
4Curvilinear coordinates — Curvilinear, affine, and Cartesian coordinates in two dimensional space Curvilinear coordinates are a coordinate system for Euclidean space in which the coordinate lines may be curved. These coordinates may be derived from a set of Cartesian… …
5Orthogonal coordinates — In mathematics, orthogonal coordinates are defined as a set of d coordinates q = (q1, q2, ..., qd) in which the coordinate surfaces all meet at right angles (note: superscripts are indices, not exponents). A coordinate surface for a particular… …
6Oblate spheroidal coordinates — Figure 1: Coordinate isosurfaces for a point P (shown as a black sphere) in oblate spheroidal coordinates (μ, ν, φ). The z axis is vertical, and the foci are at ±2. The red oblate spheroid (flattened sphere) corresponds to μ=1, whereas the blue… …
7Paraboloidal coordinates — are a three dimensional orthogonal coordinate system (λ,μ,ν) that generalizes the two dimensional parabolic coordinate system. Similar to the related ellipsoidal coordinates, the paraboloidal coordinate system has orthogonal quadratic coordinate… …
8Bipolar coordinates — are a two dimensional orthogonal coordinate system. There are two commonly defined types of bipolar coordinates. [http://bbs.sachina.pku.edu.cn/Stat/Math World/math/b/b233.htm Eric W. Weisstein, Concise Encyclopedia of Mathematics CD ROM, Bipolar …
9Ellipsoidal coordinates — are a three dimensional orthogonal coordinate system (λ,μ,ν) that generalizes the two dimensional elliptic coordinate system. Unlike most three dimensional orthogonal coordinate systems that feature quadratic coordinate surfaces, the ellipsoidal… …
10Conical coordinates — Coordinate surfaces of the conical coordinates. The constants b and c were chosen as 1 and 2, respectively. The red sphere represents r=2, the blue elliptic cone aligned with the vertical z axis represents μ=cosh(1) and the yellow elliptic cone… …
