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).

learn more… | top users | synonyms

-1
votes
2answers
81 views

Volume of solid by Spherical

Trouble setting up the integrals for this problem. Find the volume of the solid bounded by $x^2 + y^2 = 1, z = 0$, $z = 6$, $y\geq 1/2$. Use integration with Spherical coordinates. (Hint: Use two ...
0
votes
1answer
43 views

Short question about spherical coordinates

If I have a vector orthogonal to the $x$-$y$ plane of an $xyz$ axis system, I mean, a vector with just $z$ component: How can I express it in spherical coordinates?
2
votes
1answer
77 views

Calculus 3 Spherical coordinates: I'm not sure how to set this up.

find the volume of the region enclosed by the sphere $x^2+y^2+z^2=324$ and the cylinder $(x-9)^2+y^2=81$ by using spherical coordinates. I'm just not seeing how to convert this into a form where ...
4
votes
2answers
299 views

Integrating a jacobian to find the volume.

I want to solve the following: Prove that $$\displaystyle \int_R \sin^{n-2}\phi_1 \sin^{n-3}\phi_2\cdots\sin \phi_{n-2} d\theta d\phi_1\cdots d\phi_{n-2} = \frac{2\pi^{n/2}}{\Gamma(n/2)}$$ where $ ...
0
votes
0answers
25 views

Computing the spherical coordinates in n-dimensions [duplicate]

This time I want to compute the Jacobian of the spherical coordinates in n dimensions, so it needs to give me the following result: $$\displaystyle ...
3
votes
1answer
50 views

How to compute the following Jacobian

I need to show that the Jacobian of the n-dimensional spherical coordinates is $$\displaystyle r^{n-1}\sin^{n-2}\phi_1\sin^{n-3}\phi_2\cdots\sin\phi_{n-2}$$ then I have computed the Jacobian matrix, ...
0
votes
0answers
40 views

Translation matrix in spherical coordinates system

I'm using WorldWind software to draw segments (polyline) on the globe to materialize an aircraft flightplan. Each point in a flightplan is named waypoint. Waypoints are expressed in geographical ...
0
votes
1answer
88 views

sphere-sphere intersection

Let $ S_1 : (x-1)^2 +y^2+z^2=1 $ $S_2 : x^2 +y^2 +z^2 =1$ $S_3 : (x+1)^2 +y^2 +z^2 =1 $ Find the volume of the solid inside $S_2$ and outside $S_1$ and $S_3$, using triple integrals. I have try ...
0
votes
1answer
32 views

x1, y1 and radius are given - can anything be assumed about x2, y2?

I have a list of lat/lng coordinates. Given the coordinates x1, y1, and a radius r -- is there anything I can assume about the coordinates that fall within the radius of x1, y1? For example, can I ...
0
votes
0answers
105 views

Does anybody know how to actually derive spherical harmonics in a way that is historically accurate and intuitive?

And by "historically accurate", I mean without resorting to techniques of derivation which were developed after the fact or explanations which use the very concept they're trying to explain. The few ...
0
votes
1answer
73 views

Find geo coordinate by a coordinate and an angle

I need some help with this problem. I have a GPS coordinate and an angle in degrees. I need a new GPS coordinate x km away from the point I already have. Degree is counted clockwise and y-axis is ...
1
vote
1answer
41 views

Spherical Coordinates ( plane y = -x)

I am attempting to express the plane y = -x in spherical coordinates. Is there any clean way to do this? I have expressions for rho, theta, and phi in my text book but I don't think anyone of those ...
3
votes
0answers
98 views

On the equidistant distribution of $n$ points on a sphere $S^2$ by algorithm and their “validity” measures by statistical methods

I have found an algorithm for distributing $n$ points $P_0, P_1, ..., P_n$ (approximately) equidstantly on a sphere where $$\varphi_i = \pi(\phi - 1)i \qquad \theta_i= \mathrm {asin} (2i/n - 1), ...
2
votes
2answers
32 views

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 ...
2
votes
0answers
74 views

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 ...
0
votes
1answer
97 views

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 ...
1
vote
1answer
146 views

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 ...
0
votes
0answers
104 views

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 ...
1
vote
0answers
134 views

distance in n-dimensional space

According to answer of this question : Distance between 2 points in 3D space (in spherical polar coordinates) The distance between 2 points in 3 dimensional space is : $$ ...
1
vote
2answers
212 views

Solving a non-linear, multivariable system of equations

I'm researching the mathematics behind GPS, and at the moment I'm trying to get my head around how to solve the following system of equations: $\sqrt{(x-x_1)^2+(y-y_1)^2+(z-z_1)^2}=r_1$ ...
0
votes
3answers
124 views

The geometric meaning of certain mappings written in cylindrical or spherical coordinates

What is the geometric meaning of the following mappings, that are written in cylindrical coordinates? The mappings are: $$(r, \theta, z) \rightarrow(r, \theta , -z) \\ (r, \theta , z) \rightarrow (r, ...
0
votes
3answers
52 views

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 ...
0
votes
1answer
78 views

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, ...
0
votes
1answer
78 views

$\delta$ 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 ...
0
votes
1answer
109 views

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 ...
0
votes
1answer
996 views

Finding the (unit) direction vector given azimuth and elevation

I want to calculate a unit direction vector of a direction with given the azimuth and elevation (cf. http://en.wikipedia.org/wiki/Azimuth), respectively $$\alpha \in [0^{\circ},360^{\circ}), \qquad ...
1
vote
1answer
68 views

Convert $x^2+y^2+z^2=49$ to spherical coordinates

I really need your help to convert this $x^2+y^2+z^2=49$ to spherical coordinates. I tried it and I got $(R\sin\phi\cos\theta)^2+(R\sin\phi\sin\theta)^2+(R\cos\phi)^2=49$. But it says that it is ...
0
votes
2answers
29 views

Spherical distance

The spherical distance between two points (P1=(0,0,1) P2=($\frac{1}{2\sqrt{2}}$,$\frac{1}{2\sqrt{2}}$,$-\frac{\sqrt{3}}{2}$) ) is $\frac{5\pi }{6}$ I am at a loss as to how the spherical distance was ...
0
votes
2answers
314 views

Mapping Coordinates on a Plane Tangent to a Sphere into Cartesian Coordinates in 3D Space

Before we begin, I must ask you to keep the vocabulary at high school level. These variables define the point the plane needs to be tangent to – the center of the circle is at the origin. r - defines ...
1
vote
1answer
255 views

Center of mass of a trick sphere-cone intersection

B is the solid region occupying the space situated inside the sphere of radius R centered at the origin and above the cone of equation $z = \sqrt{x^2 + y^2}$. The B density is proportional to the ...
0
votes
2answers
237 views

How do I calculate opposite / most distanced coordinates on the earth?

If i get this coordinates: City Coordinates: 43°52′0″N 18°25′0″E φ Latitude °N, λ Longitude °E (of Map center): (43.8562586, 18.413076300000057) How do i determine most distant / opposite ...
0
votes
1answer
733 views

Drawing ellipse as google.maps.Polygon with 8 points

In a web page using Google Maps JavaScript API v3 (including Geometry library) I currently draw an ellipse as a "diamond" with 4 corner points by the following JavaScript code: ...
1
vote
0answers
34 views

How do you represent a vector that points to an arbitrary point on a sphere of radius R?

Is it just $$v = R \hat{r} + \theta\hat{\theta} + \psi \hat{\psi}$$ That doesn't seem right as the unit is not correct.
0
votes
1answer
29 views

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 ...
1
vote
1answer
92 views

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 ...
0
votes
1answer
53 views

Cartesian to spherical coordinate system

Hey I want to convert Cartesian to spherical coordinate system. I referred many site and for calculating elevation angle $\theta$ from positive z axis they all used formula $\arctan \frac { ...
1
vote
1answer
71 views

Surface integral of $x^4+y^4+z^4$ over the sphere $x^2+y^2+z^2=a^2$

After doing regular methodology have reached upto integral shown in figure , but when i eliminate z from it it becomes very complicated to solve .Is there any other way to solve this .Thanks
1
vote
1answer
50 views

Area of surface parametrized in spherical coordinates

Suppose we have a smooth, bounded, closed surface in $\mathbb{R}^3$ which can be parametrized by giving the distance from the origin as a function $r(\varphi,\theta)$ of spherical angles ...
2
votes
2answers
54 views

How to tell if two spherical coordinates lie on the same plane

I have the rho, theta, and phi values of two points, how can one tell that two vectors are normal to the same plane by looking at their spherical coordinates?
1
vote
1answer
387 views

Set up integral in spherical coordinates outside cylinder but inside sphere

I have the equation of a cylinder and the equation of a sphere given: Cylinder: $x^2+y^2=4$ Sphere: $x^2+y^2+z^2=25$ I'm asked to set this up in cylindrical and spherical coordinates. Cylindrical ...
0
votes
1answer
409 views

Finding the volume between a cone and a sphere

I have to find the volume between the sphere $x^2+y^2+z^2=1$ and below the cone $z=\sqrt{x^2+y^2}$ using Spherical Coordinates. Here is what I have so far: Transforming the cone part gives: ...
1
vote
1answer
103 views

3D rotational matrix between two spherical co-ordinate systems.

So I have a classical mechanics problem where I have worked out the azimuthal and altitude angle for a vector, I then want to apply rotational matrices so that the vector is realigned with the z axis ...
2
votes
1answer
42 views

Triple Integrals: Conversion

I'm currently in second year calculus and have come across a problem that I'm struggling badly to try and understand. The question is as follows: Sketch the region of integration of the following ...
1
vote
1answer
57 views

Convert from Spherical to Cylindrical Coordinates

The following integral is given in Spherical Coordinates, which procedure should I follow to express it in Cylindrical Coordinates? $$\int_{0}^\pi \int_{\frac{\pi}{6}}^{\frac{\pi}{2}} ...
3
votes
1answer
105 views

Formula for Determinant of Vectors given in spherical coordinates

In 2D, one has an easy formula for the determinant of two vectors given in spherical coordinates, i.e. $\begin{vmatrix} \cos(\phi_1) &\cos(\phi_2)\\ \sin(\phi_1) &\sin(\phi_2)\end{vmatrix} ...
1
vote
0answers
49 views

Parameterization of a closed curve on a sphere

I'm looking for a parameterization of a closed curve C on a sphere. assume the projections of C on y-z, x-z, x-y plane are f(x), g(y), h(z), respectively, and ${\oint}f(x)dx={\oint}g(y)dy=0$, and ...
1
vote
1answer
71 views

convert triple integral $\int_{-6}^{6}\int_{-\sqrt{36-x^2}}^{\sqrt{36-x^2}}\int_{x^2+y^2}^{36}x\,dz\,dy\,dx$ to spherical coordinates

I need to convert the following integral from rectangular to spherical coordinates $$ \int_{-6}^{6}\int_{-\sqrt{36-x^2}}^{\sqrt{36-x^2}}\int_{x^2+y^2}^{36}x\,dz\,dy\,dx $$ I am able to convert it to ...
5
votes
2answers
4k views

Rotation matrix in spherical coordinates

When given arbitrary point on a unit sphere $a = (\theta, \phi)$ and an arbitrary axis $\vec{A}=(\Theta, \Phi)$, can we have an algebraic expression for $a_1=(\theta_1, \phi_1)$ which is a rotation of ...
1
vote
2answers
48 views

Solve double integral

$$ \int_0^2 \int_0^{4-x^2} \frac{xe^{2y}}{4-y} \, dy\, dx $$ I'm stuck with this problem. I think I should change it so I integrate with respect to $dx \, dy$ but I'm not sure. Any help? Thanks
0
votes
1answer
37 views

Spherical coordinates on cartesian straight lines

I'm trying to solve this problem: Compute the volume of the solid bounded by: the surface $(z+1)^2=x^2+y^2,$ the surface $4z=x^2+y^2,$ above the $xy$ plane. I want to do it with spherical ...