# 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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### 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:...
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### Volume Between Spheres – Spherical Coordinates

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 ...
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### University level triple integration problem help. [closed]

Use spherical coordinates to find the volume of the solid enclosed by the sphere $x^2+y^2+z^2=4a^2$ and the planes $z=0$ and $z=a$.
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### Sum of two vectors in spherical coordinates. [duplicate]

What is the sum of two vectors in spherical coordinates? The coordinate system: Assume we have vectors $(r_1,\theta_1,\phi_1)$ and $(r_2,\theta_2,\phi_2)$ in spherical coordinates. I know the sum ...
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### find a solution for an integration in spherical coordinates

This problem comes from computation of magnetic field. $\vec r'$ and $\vec r$ are vectors, and represent different variable respectively. The integration is for $r'$ in Volune $V$'. Thank you!
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### Spherical distance between two points in terms of latitude and longitude

I have seen the answer to this question - Great arc distance between two points on a unit sphere However in a fortran program that I have this is the code to calculate spherical distance between two ...
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### Project a line onto a sphere to calculate parameterized spherical coordinates

I have a line segment and I want to find the arc that it projects to on a sphere. I know there are two arcs; I'm interested in the one that's closest to the line (or intersects it). The easy way to ...
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### Dual Spaces vs Dual Bases

I'm trying to wrap my head around differentiable manifolds and tensors. I partially worked through a question which asked me to use the metric tensor and the line element in spherical polar ...
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### Marsden Triple Integration, Spherical Coordinates

This comes from Marsden Vector Calculus book. I think I've done it correctly, but I'm not very confident in my work. The integral is \int_0^3\int_0^\sqrt{9-x^2}\int_0^\sqrt{9-x^2-y^2} \frac{\sqrt{x^...
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### How to integrate a part of a sphere limited by a rectangle?

I have a function which depends on the solid angle $\frac{df}{d \Omega} = \frac{df}{d\phi d\theta}$. I want to integrate it over a part of the sphere limited by a rectangle. How should I set the ...
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### Coordinate system for evenly-distributed points on a sphere

Suppose I have a sphere with a set of evenly-distributed points on its surface: What is the coordinate system to use to represent these points, where each adjacent point is a unit step? Spherical ...
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### Relationships between positions on a sphere in a global coordinate system

Imagine I have a camera which is observing an object. The camera can move around the abject, by traversing a virtual sphere, where the radius of the sphere is the distance between the object centroid ...
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### First person camera rotation (conversion between spherical to cartesian coordinates)

A similar question has been asked before on Stack Overflow but no satisfying answer. Basically I'm following this tutorial, and I can't exactly figure out how the guy deduced these two equations to ...
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### Triple integral in spherical coordinates: Finding $\phi$ limits?

The question asks to convert to spherical coordinates then evaluate. So for this question, I manage to get the bounds of theta and row right, but I got the bounds of phi wrong. According to the ...
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### Is it possible to calculate the lat/lon of a point knowing the extent coordinates?

I would like to know where it's possible to determine the latitude and longitude corresponding to a point inside a cartesian (planar?) representation of a geographical map, knowing the x/y coordinates ...
Given is this operation $\left((\mathbb{1}-\hat{r}\hat{r})\cdot \nabla\right) \cdot v(r) = \left(\nabla-\hat{r} (\hat{r} \cdot \nabla)\right) \cdot v(r)$, where $r=(x,y,z) \in \mathbb{R}^3$, \$\hat{...