# Tagged Questions

Questions on spherical coordinates, a three-dimensional coordinate system where a point is represented in terms of its distance from the origin, and its latitude and longitude angles (or complements thereof).

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### Evaluating integrals in R^m

Let $|\cdot|_m$ denote the Euclidean norm in $\mathbb{R}^m$. Then I wish to prove that $\displaystyle\int\limits_{\mathbb{R}^m}|x|_me^{-|x|_m}dx<\infty$ It's kinda embarrassing to say this, but ...
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### Parametrization of sphere including constant inclination $(\theta, i)$ geodesics

Find parametrization of sphere with respect to $\theta$ = constant meridians and i = constant inclination geodesic circles passing through N-S axis and E-W axis respectively. The Earth does not rotate ...
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### Can anyone check if this correct?

Convert to spherical coordinates and evaluate:$$\iiint_{E}z(x^2+y^2+z^2)^{-3/2}dV$$ where E is the region satisfying the following inequalities:$$x^2+y^2+z^2\le16,z\ge 2$$ This is what i have done so ...
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### Cartesian to Spherical Coordinate Conversion for Triple Integral

I have a question regarding what happens to the boundaries when converting a triple integral from Cartesian to Spherical Coordinates. Example ...
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### Manifolds, coordinate systems, books

Which books, say Lee's Introduction to Smooth Manifolds or Munkres' Analysis on Manifolds explains how the theory of a differentiable manifolds can be used to solve a problem that is expressed in a ...
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### Solutions of the Laplace Equation in spherical coordinates

I would like some help with the following problem. Thanks for any help in advance. Use spherical coordinates to find all solutions of the Laplace equation ∆u(x)=0, u∈Ω⊂R3 that depend only on the ...
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### Cylindrical - Spherical coordinates

We are given a point in cylindrical coordinates $(r, \theta , z)$ and we want to write it into spherical coordinates $(\rho , \theta , \phi)$. To do that do we have to write them first into ...
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### Radius of the Earth at N32.704220, W90.000000?

I want to express a point on a map in radian spherical coordinates. By Google maps, this location is north of Canton, MS, USA just a few hundred feet from US 51. In radian spherical coordinates, ...
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### $\delta$ in spherical coordinates: $\int_0^R\int_0^{2\pi}\int_0^{\pi}\delta(\theta-\pi/2)(r^2\sin(\theta)\,d\theta \,d\phi \,dr)$

Suppose you have a disc of radius $R$, we can find its area in polar coordinates by: $$\int_0^R\int_0^{2\pi}(r\,d\phi \,dr)=\pi r^2$$ Naively, I also expect to be able to integrate in spherical ...
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### Intensity distribution of a Lambertian LED as a function of angle

I have a practical spherical geometry problem that I'm having trouble cracking. I'm illuminating a planar surface with an LED that has a Lambertian intensity distribution, i.e. the intensity drops off ...
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### Transform Confocal Ellipsodal to Spherical Coordinates

I heard that someone published a paper showing that the confocal ellipsoidal coordinate system can transform into the spherical coordinates under special limit evaluations, however I was unable to ...
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### Writing same equation in different forms

I am working with a unit circle with imaginary integration. I know from experience that this can be written as $f(\theta)=\cos t+ i \sin t$ or $e^{i \theta }$ My question would be if i have a circle ...
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### Vector flux through a segment of a sphere

Given the vector field $\vec A(\vec r) = \vec r$, I have to calculate the vector flux through a sphere whose center is located in the origin. I want to apply Gauß-Theorem and use spherical ...