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Direct solution of the equations is difficult, however, in part because the separation constants and appear simultaneously in all three equations. Following the above approach, paraboloidal coordinates have been used to solve for the electric field surrounding a conducting paraboloid. [4]
On the axis of a circular paraboloid, there is a point called the focus (or focal point), such that, if the paraboloid is a mirror, light (or other waves) from a point source at the focus is reflected into a parallel beam, parallel to the axis of the paraboloid. This also works the other way around: a parallel beam of light that is parallel to ...
A circular paraboloid is theoretically unlimited in size. Any practical reflector uses just a segment of it. Often, the segment includes the vertex of the paraboloid, where its curvature is greatest, and where the axis of symmetry intersects the paraboloid. However, if the reflector is used to focus incoming energy onto a receiver, the shadow ...
The red paraboloid corresponds to τ=2, the blue paraboloid corresponds to σ=1, and the yellow half-plane corresponds to φ=-60°. The three surfaces intersect at the point P (shown as a black sphere) with Cartesian coordinates roughly (1.0, -1.732, 1.5).
In mathematics, a chaotic map is a map (an evolution function) that exhibits some sort of chaotic behavior.Maps may be parameterized by a discrete-time or a continuous-time parameter.
Circular paraboloid (red) and its truncated reflector (green). In a parabolic antenna, the feed horn is placed at the focal point and irradiate the reflector. The latter send back in space a highly focused parallel beam that one can describe as pencil shape. When one removes a section of the paraboloid, rays coming from that section are lost ...
This page was last edited on 14 June 2010, at 20:13 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may ...
In geometry, a hyperboloid of revolution, sometimes called a circular hyperboloid, is the surface generated by rotating a hyperbola around one of its principal axes. A hyperboloid is the surface obtained from a hyperboloid of revolution by deforming it by means of directional scalings , or more generally, of an affine transformation .