# 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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### Great circle distance on an ellipsoid [on hold]

Let's say I have a set of latitude and longitude (B,L on a reference ellipsoid WGS-84) and I also know the great circle distance (both in radians and meters) from my point to some point X on a sphere ...
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### Create 3d rotation matrix given spherical coordinates? [on hold]

Is it possible to form a 3d rotation matrix given a spherical coordinates $\theta$ and $\phi$ ?
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### Plotting Spherical Coordinates

I'm trying to plot the Poisson Kernel, where a = 1, so the resulting equation would be $$P(r,\theta) = \frac{1-r^2}{1-2r\cos(\theta)+r^2}$$ $0\leq r <a = 1 ,\textrm{ } -\pi \leq \theta \leq \pi$ ...
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### Sperical coordinates and the divergence theorem

Use the divergence theorem to calculate $\int \int F\cdot dS$ where $F=<x^3,y^3,4z^3>$ and $S$ is the sphere $x^2+y^2+z^2=25$ oriented by the outward normal. I have found that ...
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### Point along great circle line (aka arc) closest to a target point on the ground

Given: an arc (aka a great circle line, not a straight-line) defined by two arbitrary end points (which I can express in lat/lon/altitude or earth-centered fixed (ECF) 3D 'cartesian' space). Think ...
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### Getting topological objects from the “cube” of $T^3$

One can imagine $T^3$ much like he can imagine $T^2$: as a flat box with opposite faces identified. One may put coordinates on $T^3$, each of which would logically range from $0$ to $2\pi$. To get ...
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### Computing the vector Laplacian in spherical coordinates using metric tensor

I want to compute the Laplacian of a vector in spherical coordinates using metric tensor. I started only with the first component but I have obtained a different formula! Let be $\vec{v}$ a vector ...
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### Equation of a circle in spherical coordinates

What would be the equation of an arbitrary circle rotated along some angle theta around the X-axis in spherical coordinates? For simplicity we may assume that it is a circle with constant radius r. ...
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### Find the volume of a shape using spherical coordinates.

Find the volume of the shape formed inside $x^2+y^2=z$ and $x^2+y^2=2$ using spherical coordinates. I know I need to do a triple integral but I can't quite get the integral limits.
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### Using the Dirac delta function to find the density of point masses/charges

Here is an example from a textbook: Suppose there is a unit charge or unit mass at the point $(x,y,z)=(-1,\sqrt{3},-2)$; then in rectangular coordinates, the ...
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### What does this triple integral in spherical coordinate represent?

$$\int_{0}^{a}\int_{0}^{2\pi}\int_{0}^{2\pi} r(b+r \cos\phi) d\phi d\theta dr$$ What does the above integral represent? I don't think it's volume of a figure, since either $\phi$ or $\theta$ should ...
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