Skip to main content

# Questions tagged [spherical-coordinates]

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).

1,571 questions
Filter by
Sorted by
Tagged with
1 vote
0 answers
35 views

0 votes
0 answers
63 views

### Vector field of rotation around an axis in spherical coordinates

This is a qualifying exam question in Differential Geometry. I'm new to the subject and am reading up from John Lee's Introduction to Smooth Manifolds. Let $M=S^2\subset\mathbb{R}^3$ be the unit ...
0 votes
0 answers
24 views

### How to define complex valued spherical coordinates?

I am currently tackling an optimization problem involving complex valued vectors. However the optimization is solely about finding the optimal "direction" of the vector. So any (complex-...
0 votes
1 answer
65 views

### Why couldn't I correctly use the spherical coordinate system when calculating this surface intergral?

The problem I've been trying to solve is this: Consider sphere surface $\Sigma: x^2+y^2+z^2=2ax(a \gt 0)$, find surface integral: $\iint_{\Sigma}(x^2+y^2+z^2)dS$. What I tried to do is to first ...
0 votes
1 answer
63 views

• 3,045
0 votes
0 answers
18 views

### Series Solution of Laplace Equation in Spherical Coordinates

I am a physics student and this question was asked on the Physics stack exchange as well. I just want you to go through the derivation first. I was recently Studying Griffiths Electrodynamics after a ...
0 votes
0 answers
12 views

### Three dimensional spherical interpolation like trilinear interpolation

Say we have a 5x5x5 grid where a quaternion, q, exists at every point. The objective is to express the distribution of quaternions in a functional form in terms of the positions, i.e. q(x,y,z) = Ax + ...
0 votes
0 answers
72 views

### How to find the tangent when converting from 2D angles to Spherical to Cartesian coordinates?

I am making a spherical/ball-in-socket joint, and I want to limit the movement of the bodies relative to each other. The limit is defined as 2 angles $\alpha$ and $\beta$ which make a 2D rectangle. I ...
1 vote
1 answer
25 views

• 531
0 votes
0 answers
8 views

### Given a vector field in spherical coordinates, compute the flux through a disk at z = -d

I want to compute the flux of the magnetic field $B = \frac{\mu_0m}{4\pi r^3}(2cos(\theta)\vec{e_r}+sin(\theta)\vec{e_\theta})$ through the disk at $z=-d$ with radius b centered around the z-axis. ...
0 votes
2 answers
42 views

### Orthographic Projection and Concentric Circles [closed]

Let $C$ be the bounded set of concentric circles centered at the origin. Let $r_n = \sqrt{\frac{n}{\pi}}$ for any integer $n \in [1, k]$ be the radius of the circle $C_n \in C$. Assume $C$ is a ...
• 115
2 votes
1 answer
67 views

### Integration by substitution in Selberg's Integral

I am reading the article "Hilbert--Schmidt volume of the set of mixed quantum states" (https://arxiv.org/abs/quant-ph/0302197). I do not understand the step in which we start from (4.2) and ...
• 740
2 votes
1 answer
65 views

### What coordinate substitution should I perform to evaluate this triple integral?

I am trying to evaluate the following triple integral: $$\int_{-1}^1 \int_{-\sqrt{4-4x^2}}^{\sqrt{4-4x^2}} \int_{\sqrt{4x^2 + z^2}}^2 ye^{4x^2 + y^2 + z^2} \, dy\, dz\, dx$$...
1 vote
0 answers
52 views

### Is this the correct equation for divergence of a horizontal vector field in spherical coordinates?

There is a Horizontal vector field $\textbf{V} = <u\hat{\lambda}+v\hat{\theta_{lat}} + 0\hat{\textbf{r}}>$ which is gridded along Earth's surface. Physically speaking, the vector field's ...
• 531
0 votes
1 answer
140 views

### How do I solve for surface area in this case?

Okay, I have the parametric equation in spherical coordinates for a sphere, a cone tangent to that sphere and a circle inclined with an angle $\Omega$ to the $zy$ plane. ( Desmos graph link ). I need ...
0 votes
1 answer
57 views

• 43