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paraboloidal

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paraboloidal
paraboˈloidal, a. [f. as prec. + -al1.] Of the form of a paraboloid.1825 J. Nicholson Operat. Mechanic 575 Circular [domes] may be spherical, spheroidal, ellipsoidal, hyperboloidal, paraboloidal, &c. 1876 G. F. Chambers Astron. 759 Using, instead of a spherical, a paraboloidal speculum. Oxford English Dictionary
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Paraboloidal coordinates
Paraboloidal coordinates are three-dimensional orthogonal coordinates that generalize two-dimensional parabolic coordinates. For instance, the Laplace equation and Helmholtz equation are both separable in paraboloidal coordinates. wikipedia.org
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Paraboloidal Coordinates How would one find the transforms for paraboloidal coordinate systems. ie) I want to find $x,y$, and $z$ in terms of other variables so that I can use the Jacobian to find the differential vol...
If you use cylindrical coordinates \begin{align} x &= r \cos \theta \\\ y &= r \sin \theta \\\ z &= z \end{align} then $$ z = 16 - r^2 $$ and $$ \frac{D(x,y,z)}{D(r,\theta,z)} = r. $$ which leads to a pretty easy volume calculation (if top and bottom of paraboloid are simple enough).
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Paraboloid
Dimensions of a paraboloidal dish The dimensions of a symmetrical paraboloidal dish are related by the equation where is the focal length, is the depth The volume of the dish, the amount of liquid it could hold if the rim were horizontal and the vertex at the bottom (e.g. the capacity of a paraboloidal wikipedia.org
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Using paraboloidal coordinates I have the 3-dimensional paraboloidal coordinates $$s_{\pm}=\sqrt{x^2+y^2+z^2}\pm z$$ $$\phi=ArcTan(y/x)$$ with the inverse transformation $$x=\sqrt{s_+ \cdot s_-}\cdot cos(\phi)$$ $$y=...
\end{eqnarray} $$ These coordinates are known as _Paraboloidal_ coordinates $(\phi,u,v)$. We can call then the _partly squared paraboloidal_ or the _NicoDean_ coordinates...
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Parabolic reflector
A parabolic (or paraboloid or paraboloidal) reflector (or dish or mirror) is a reflective surface used to collect or project energy such as light, sound Ideally, the reflector would be exactly paraboloidal at all times. wikipedia.org
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paraboloid
paraboloid, n. (a.) Geom. (pəˈræbəlɔɪd) Also 7 -oeides, -oeid, 8–9 -oide. [In form, ad. Gr. παραβολοειδής a. (in a different sense), whence in 17th c. use paraboloeides: see parabola and -oid, and cf. F. paraboloïde.] † 1. A parabola of a higher degree: = parabola b.1656 Hobbes Six Lessons Wks. 1845... Oxford English Dictionary
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Adivar (crater)
A darker streak, in a horseshoe or paraboloidal shape, surrounds the bright area. Radar-dark (i.e., smooth) paraboloidal streaks were observed around craters in earlier Magellan images, but this is a rare bright crater streak. wikipedia.org
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parabolize
parabolize, v. (pəˈræbəlaɪz) [See -ize.] 1. a. trans. To express or represent parabolically; to set forth in a parable. Also absol.1600 W. Watson Decacordon (1602) 20 Otherwise could not the church Catholike be..parabolized with a net cast into the sea. Ibid. 34 As our Sauiour Christ rightly parabol... Oxford English Dictionary
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Rotating furnace
The same process can be used to make a lens with a concave paraboloidal surface. By placing the container away from the axis, off-axis paraboloidal segments can be cast. wikipedia.org
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COSMOSOMAS
Both instruments are based on a circular scanning sky strategy, consisting of a 60 rpm spinning flat mirror directing the sky radiation into an off-axis paraboloidal wikipedia.org
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CN206431372U - 一种全反射式消光晕光束匀化光学系统 - Google Patents
CN206431372U CN201720138311.3U CN201720138311U CN206431372U CN 206431372 U CN206431372 U CN 206431372U CN 201720138311 U CN201720138311 U CN 201720138311U CN 206431372 U CN206431372 U CN 206431372U Authority CN China Prior art keywords mirror axis paraboloidal lens array hyperboloidal paraboloidal mirror Prior art date 2017-02-16 Legal status (The legal status is an assumption and is not a ...
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Volume integral of grad Could someone explain to me what it means to do a volume integral over a vector field. It doesn't seem to make sense! I have attached the question but don't understand what the last part "means...
One way to calculate a volume integral of a vector field $\mathbf{u}(\mathbf{x})$ is to expand $\mathbf{u}$ into its Cartisian components: $\mathbf{u}(\mathbf{x})=\mathbf{\hat e}_xf(\mathbf{x})+\mathbf{\hat e}_yg(\mathbf{x})+\mathbf{\hat e}_zh(\mathbf{x})$, where $f,g,h$ are scalar fields. Then by l...
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Jan van der Molen
He later assisted with the computer-aided design of the concrete hyperbolic-paraboloidal Rosebud Sound Shell with local architect Ronald F Murcott, and This employed sophisticated hyperbolic-paraboloidal platforms to allow large trees to be planted on its roof. wikipedia.org
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Solar cooker
It remains paraboloidal, but its focal length and other parameters change as it tilts. The mirror is never exactly paraboloidal, but it is always close enough for cooking purposes. wikipedia.org
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