# 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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### Let $r(s)$ be a regular closed curve that is in the sphere $S^2$. Prove that $\int_{\gamma}\tau(s)ds=0$ $\gamma$-map of this curve, $\tau$ torsion

Let $r(s)$ be a regular closed curve that is in the sphere $S^2$. Prove that $$\int_{\gamma}\tau(s)ds=0$$ $\gamma$-map of this curve, $\tau$ the function of torsion of this curve. Every year this ...
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### Minimizing arc length on unit sphere (geodesics)

I just completed a Calculus IV course and taught myself basic Calculus of Variations, and wanted to extend some of the basic principles of optimization from planes to surfaces. The arc length ...
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### Trajectory on a sphere

I've asked a question before concerning a parallel problem, and I read a wikipedia page on spherical caps (Nominal Animal), which gave me an idea to do the following: I have the Cartesian coordinates ...
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### Is there a solution to the equation $tan({\phi})=\frac{0}{0}$

I've been reading about conversion from Cartesian ($x,y,z$) to Spherical (r, $\theta$, $\phi$) coordinates. The formula to find the value of ${\phi}$ is given as: $\tan({\phi})=\frac{y}{x}$ My ...
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### Find the Radius of Sphere using TDOA

My goal is to calculate Position of impact using Trilateration. I followed this guide on wikipedia : Trilateration Wikipedia I don't know how to find the Radius R1,R2,R3.(Normally it is PA,PB,PC,...
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### The smallest bounding sphere of a prolate spheroid domain

Let $\Omega\subset \mathbb{R}^3$ be a prolate spheroid domain. Denote by $d$ its interfocal distance and by $b$ the surface of the region occupied by $\Omega$. The question is how to prove that the ...
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### Angle between arc of two points on a unit sphere and $xy$-plane [closed]

Suppose I have two points on a unit sphere whose spherical coordinates are $A(\theta_1,\phi_1)$ and $B(\theta_2,\phi_2)$, what is the angle between $xy$-plane and arc $AB$? Maybe I can draw a ...
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### Conversion of laplacian form cartesian to spherical coordinates 2nd part

Using the same method of conversion of laplacian from cartesian to spherical coordinates and changing $\psi$ to $u$, I am trying to finish the demostration of the spherical laplacian. However, I have ...
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### Estimating the distance between two coordinates but without using Euclidean distance

Bill opens up "Café Finder" on his phone, and it tells him that it will take him 10 minutes to get to his nearest Starbucks to grab a triple-shot frapa-crapa-flat-white, so he decides to walk. 20 ...
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I'm not sure how to approach the problem, though I know it needs to be broken up into two integrals before it can be evaluated based on the way the answer input is set up. I do not know how to start ...
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### Find a circle on sphere using spherical distance

I have a sphere with radius $R$. On this sphere I also have a point $P_1$ written in spherical coordinates, so I know $\theta_1$, $\phi_1$ and $R$ for this point (same as on this picture). I also ...
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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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### Equation used to represent a disc galaxy

I'm trying to create a solid which looks something like a disc galaxy: Key features are: Bulge in the middle Tapered "width" as it extends to a disc shape The end goal would be to use Python to ...
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### rotation of spherical surface in spherical coordinates

I need to plot a spherical surface in computer (like the surface of a lens). I know the normal vector (as an example, say $\ n=(1,2,3)$) of this surface and it originates from the centre of the ...
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### rotate a scalar valued spherical function

I want to rotate a function $f(\theta,\phi)$ around an arbitrary angle in 3D space. (Assuming $\phi$ is in the $xy$ plane and goes from $0$ to $2\pi$, and $\theta$ starts from $+z$ and goes from $0$ ...
### Set up triple integral's boundary for $x^{2} + (y-a)^{2} + z^{2}=a^{2}$ in spherical coordinates.
I have trouble with setting up triple integral's boundary for $\rho$. Solid object's equation is $x^{2} + (y-a)^{2} + z^{2}=a^{2}$,which is a sphere centered at (0,a,0), in spherical coordinates. Note:...
I'm trying to find the volume between the spheres: $x^2 + y^2 + z^2 = 9$ and: $x^2 + y^2 + (z-2)^2 = 9$ I have calculated this, but have a strong feeling that little of what I did was actually ...