Questions tagged [cylindrical-coordinates]
Questions on cylindrical coordinates, a coordinate system where points in space are represented by their distance to the $z$-axis ($r$), the angle the line joining the orthogonal projection of the point on the $xy$-plane and the origin makes with the positive $x$-axis ($\theta$) and the $z$ coordinate of the point.
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questions
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Cylinder geometry
I want to measure the surface contour of a cylinder. I am using a laser line scanner to measure it. I am currently facing a problem with x-tilt - a misalignment caused when the measurement laser line ...
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0answers
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L1 inner product for cylindrical coordinates
In cartestian coordinates, the L1 inner product for $f=f(x,y,z)$ is $\int_\Omega f^2 \,dx$.
What is the L1 inner product for a given function f in cylindrical coordinates $(x,y,z) = (r\sin\theta,r\cos\...
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0answers
6 views
Fast Fourier Transform in Cylindrical Coordinates
I am working in cylindrical coordinates, e.g. I have a function $(x,y,z)=(r,\theta,z)$. I would like to take a fast fourier transform in the $\theta$ direction only.
Will the fft be different than in ...
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1answer
34 views
Graph $(r-2)^2+z^2=1$
I was doing a problem and I got stuck at the step of drawing this:
$(r-2)^2+z^2=1$
Since it does not depend on $\theta$, I know it would be like a circle centered at $(2,0)$ with radius $1$ in $xz$ ...
2
votes
1answer
26 views
Triple Integral in Cylindrical Coordinates using x axis instead of z axis
Today in my Calculus class my teacher made an example using change of variables using this problem:
Find the volume of the solid inside the cylinder $y^{2} + z^{2} = 2y$ bounded by $x=0$ and the ...
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1answer
45 views
convert $(x-x')^2 + (y-y')^2 + (z-z')^2$ to cylindrical coordinates
Context
This was an interim problem related to a Green's function solution of a boundary-value problem in cylindrical coordinates. I posted this question on this forum hoping for guidance. Ultimately, ...
-3
votes
1answer
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Find the volume composed by a cylinder and a sphere [closed]
As the title says find the volume composed by a cylinder and a sphere
$$\left\{ \begin{array}
xx^2 + y^2 \geq 9 \\
x^2 + y^2 + z^2 \leq 25
\end{array} \right. $$
I want some help in this. Thank you.
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2answers
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Find the limits for the following triple integral
The problem goes as follows: $$\iiint_{\mathrm{E}}(x^2-z^2)\, dx\,dy\,dz, $$where $\mathrm{E}$ is defined by $x, y,z \ge 0$
and $x+y+z \le 1$.
I'm have difficulties finding the limits in order to ...
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1answer
28 views
Calculating the volume of a region in $\mathbb{R}^3$
We are interested in the volume of the bounded region above $z = \sqrt{3x^2 + 3y^2}$ inside $x^2+y^2+z^2=9$. To Find the volume, we need to calculate this:
$$ \iint_{x^2+y^2=3} \sqrt{9-x^2-y^2} - 3\...
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0answers
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Expanding First term of Einstein Summation to transform Cartesian System to Curvilinear System
Mathematics Post: Curl in cylindrical coordinates
Can someone expand the Einstein summation boxed in green for the first term to get a feel for the expansion?
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1answer
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How can I calculate distance from two pixels HSV?
I want to look for a better way to calculate the distance between two pixels in the HSV color space. In my program I used Euclidean distance.
$$
distance(p_1, p_2) = \sqrt{(h_1 - h_2)^2 + (s_1 - s_2)^...
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1answer
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The equation of the surface in cylindrical coordinates: ${r^{2}-2z^{2}=4r\cosĪø-8r\sinĪø-12z}$ . What is the equation in perpendicular coordinates?
The equation of the surface in cylindrical coordinates:
${r^{2}-2z^{2}=4r\cosĪø-8r\sinĪø-12z}$
i) What is the equation in perpendicular coordinates?
ii) Write it name?
My try:
I put these in the ...
2
votes
0answers
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Poisson equation in a cylinder
I need to solve the problem $\nabla^{2} u(r,\theta,z)=Q(r,\theta,z)$
inside a circular cylinder $(0 < r < a, 0 < \theta < 2\pi, 0 < z < H)$ subject to $u = 0$ on the sides.
I'm ...
1
vote
1answer
28 views
Converting $r=(x^2+y^2+z^2)^{1/2}$ cartesian coordinates to spherical coordinates
Let $r=(x^2+y^2+z^2)^{1/2}$ be the radial distance from the origin expressed in cartesian coordinates.
I have been asked to express this in cylindrical coordinates.
Is $r=(x^2+y^2+z^2)^{1/2}$ the same ...
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0answers
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Is Curl not a cross product?
I have a vector in cylindrical Coordinates:
$$\vec{V} = \left < 0 ,V_{\theta},0 \right> $$
where $V_\theta = V(r,t)$.
The Del operator in $\{r,\theta,z\}$ is: $\vec{\nabla} = \left< \frac{\...
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2answers
29 views
Volume of a cone given constraints on $z$
This question is pretty straightforward, however, it's been a couple years since I've had to solve an integral like this!
Compute the volume bounded by $x^2 + y^2 \le z^2$ such that $c_1 \le z \le c_2$...
1
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1answer
97 views
How do I convert equations from cartesian to spherical/cylindrical?
I understand the relations between cartesian and cylindrical and spherical respectively. I find no difficulty in transitioning between coordinates, but I have a harder time figuring out how I can ...
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1answer
33 views
Volume using triple integral with spherical and cylindrical coordinates [closed]
I had to solve this triple integral and I tried to solve by cylindrical and spherical coordinates but couldn't get anywhere. I was hoping someone could help me in this problem.
Solve $\int \int \int _{...
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1answer
36 views
How do I change between cartesian and cylindrical coordinate systems?
I have a vector $\textbf{D}=(x,3,5)$ in cartesian coordinates $(x,y,z)$ that I want to express in cylindrical coordinates $(r,\phi,z)$. Do I just plug the values for x,y,z into the expressions to get ...
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1answer
40 views
Volume of a solid region enclosed by elliptic cylinder using triple integral
Find the volume of a solid limited laterally by an elliptical cylinder $$\frac{(x-2)^2}{4}+\frac{(y-1)^2}{9}=1$$ and by the planes $z+x=5$ and $z+x=6$.
I tried doing by cylindrical coordinates and ...
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0answers
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Use integration by parts in cylindrical coordinates to turn these second derivatives into first derivatives
I have a complex function $\psi(\rho,z)$ in cylindrical coordinates, which has the conditions $\psi=0$ as $z\rightarrow\pm\infty$ and $\rho\rightarrow +\infty$. The quantity $E$ given by the double ...
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1answer
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Finding the volume of the solid below $z=y$ and above the region in the $xy$-plane bounded by $y=x$ and $y=x^2$. (Seeking advice on bounds.)
So, I have this question which states:
Find the volume of the solid that lies below the surface,
$$z=y$$
and above the region $T$ in the $xy$-plane enclosed by the two curves $y=x$ and $y = x^2$.
As ...
0
votes
1answer
39 views
Evaluate the volume of the solid bounded by $z=8-x^2 - y^2, z = x^2 + y^2, x = 1, y=\sqrt{3} x, y=0$
I am currently stuck on how to find the radius as shown in my xy-projection it is cut by the plane x=1. However I tried ignoring that part as I cannot find a solution for it and first tried to find an ...
0
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2answers
28 views
change of variable to get a quasi-cartesian laplace equation?
when writing the (vector) laplace equation in cylindrical coordinates in a $(r,\theta)$ plane, we get:
$$ \left( r^2\frac{\partial^2}{\partial r^2} + r\frac{\partial}{\partial r} + \frac{\partial^2}{\...
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0answers
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Triple Integral of the norm of a vector over the unit cube sat in the positive quadrant.
I saw a meme about $\int_{0}^1 \int_0^1\int_0^1 \sqrt{x^2 + y^2 + z^2} \space dx dy dz$ on Facebook (Wolfram Alpha only giving an approximate answer) and the closed form of the answer is supposed to ...
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0answers
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Rewriting equations in spherical, cylindrical coordinates
As I am studying for an exam, Iām working on converting the equation theta = pi/4, where in our book theta is the angle made by a point with the z-axis, confusingly called the āpolar angleā. Anyways, ...
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1answer
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Converting to cylindrical coordinates
The given integral is: $$\int_\frac{-\sqrt3}2^\frac{\sqrt3}2\int_\frac{1}2^\sqrt{1-x^2}\int_\sqrt{x^2+y^2}^{2-x^2-y^2} \frac{x}y dzdydx$$
I converted it as: $$\int_0^\pi \int_0^1\int_r^{2-r} \cot\...
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2answers
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Find volume using triple integration with cylindrical coordinates
Find volume of $E$ using triple integration and cylindrical coordinates, when $E$ is bounded by $$x^2+y^2=x,\quad y=0,\quad y=x,\quad z=0,\quad z=\sqrt{x^2+y^2}$$
I know that in cylindrical ...
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0answers
28 views
Convert from Cylindrical coordinate to Cylindrical vector
Let's assume there is a function of curve represented with Cylindrical Coordinate system as $r(\phi, z)$, each point can be represented as $P(r(\phi,z),\phi,z)$. I want to convert each point into a ...
0
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1answer
40 views
Transform derivatives from 2D Cartesian to axisymmetric cylindrical coordinates
Consider the 1st and 2nd derivatives (differential operations) of a function $z=f(x)$ with respect to horizontal coordinate $x$ in 2D Cartesian coordinates $(x,z)$,
$$\frac{df}{dx} \quad \text{and} \...
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1answer
36 views
Question on a triple integral
I have a triple integral $\iiint_E \sqrt{16-x^2-z^2}dV$, where $E$ is the region above the $xy$-plane, outside the cylinder $x^2+z^2=4$, and inside the sphere $x^2+y^2+z^2=16$.
I rewrite the region $E$...
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votes
3answers
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Why do each of these cylindrical triple integrals evaluate differently?
The problem in question is thus:
Find the volume cut out of the sphere of a radius $a$ centered at the origin by the polar curve $r = a\cos\theta$. I attempted to solve the problem using this ...
1
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2answers
31 views
Use cylindrical coordinates to find the volume of the solid using triple integrals
The given rectangular equations are
$$x^2+y^2+z^2=64$$
$$(x-4)^2+y^2=16$$
Converting to cylindrical coordinates I get
$$r^2+z^2=64$$
$$r=4cos(\theta)$$
So my triple integral is
$$4\int_0^{\frac{\pi}{2}...
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1answer
110 views
Convert the triple integral from rectangular coordinates to both cylindrical and spherical coordinates
The given integral is:
$$\int_{-7}^7\int_{-\sqrt{49-x^2}}^\sqrt{49-x^2}\int_{x^2+y^2}^{49}xdxdydx$$
Converting to cylindrical coordinates:
$$\int_{0}^{2\pi}\int_{0}^7\int_{r^2}^{49}r^2\cos(\theta)...
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1answer
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Cylindrical Coordinates Question on Derivation(Informal)
In cylindrical coordinates, why do we look at the distance r, which is the length from the origin to the center point of the "cylindrical cuboid's" projection onto the xy plane. In this case,...
3
votes
1answer
104 views
Evaluating $\int_{-4} ^4\int _0 ^{\sqrt{16-x^2}} \int _0 ^{16-x^2-y^2} \sqrt{x^2 + y^2}\,dz\,dy\,dx$
Question: Evaluate the given triple integral with cylindrical coordinates:
$$\int_{-4} ^4\int _0 ^{\sqrt{16-x^2}} \int _0 ^{16-x^2-y^2} \sqrt{x^2 + y^2}\,dz\,dy\,dx$$
My solution (attempt): Upon ...
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0answers
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Axisymmetric problem - two ways of deriving a (transformed) integral in cylindrical coordinates
A concise description of the problem
An integral $\left(\int_{\Omega}w\,\operatorname{div}(\operatorname{grad}(u))\right)$ should be transformed in a more convenient form and expressed in cylindrical ...
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0answers
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Decomposing Circumferential strain to Radial and Tangential coordinates
I am currently working on a problem where a cylindrical sample is being compressed (say in the z direction, vertically) causing to increase in circumference (in x-y plane).
I have a gauge which ...
0
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0answers
19 views
Hankel Transforms in cylindrical coodinates and discrete point evaluation
I'm currently reading a textbook on electromagnetism and came across this Hankel transform pair in cylindrical coordinates denoted as:
$$A(\lambda; z) = \int_0^\infty
A(r; z) J_1(\lambda r)r \, dr$$
$...
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0answers
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Eigenvalues of Schrodinger equation in cylindrical coordinates
I have Schrodinger equation of the form:
$$ \left[\frac{\partial^{2}}{\partial{r}^{2}}+\frac{1}{r} \frac{\partial^{}}{\partial{r}^{}}+\frac{1}{r^{2}}\left(\frac{\partial^{}}{\partial{\varphi}^{}}+i\...
0
votes
1answer
20 views
Different volume with cartesian and cylindrical coordinates.
I want to find the volume of the solid bounded between paraboloid $z=4-x^2-y^2$ and the plane $z=0$.
I first tried with cylindrical coordinates:
$$V=\int_{0}^{2\pi} \int_0^2 \int_0^{4-x^2-y^2} dz \rho ...
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2answers
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How can we find the limits of this integration $\iiint_{G}f(x,y,z)\,dx\,dy\,dz$ with cylindrical coordinates?
Let $$G=\left\{(x,y,z)\in\mathbb{R}^3:\ x^2+y^2+z^2\leq a^2,\ (x^2+y^2)^2\geq a^2(x^2-y^2),\ z\geq 0\right\}$$
If we apply cylindral coordinates on $G$ we have that $0\leq z \leq \sqrt{4a^{2}-r^{2}}$ ...
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0answers
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Convert the rectangular coordinates of the cone to cylindrical coords.
The height of the cone is $4$ and the radius is $2$ given by the inequality $0 \leq z \leq 4-2\sqrt{x^2 + y^2}$.
From that information we can see we have the point $(1,0,2)$ and we can use this to ...
0
votes
1answer
184 views
Convert function from cartesian coordinates to cylindrical and spherical
Introduction
I have a point charge of magnitude $-6Q_0$. This point charge is placed in the origin of an orthogonal coordinate system. The electric field at a arbitrary point $P=(x,y,z)$ caused by ...
1
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1answer
54 views
Deriving the new differential wave equation when assuming cylindrical symmetry
We have the differential wave equation
$$\dfrac{\partial^2}{\partial{r}^2}(r \psi) = \dfrac{1}{v^2} \dfrac{\partial^2}{\partial{t}^2}(r\psi).$$
If we assume cylindrical symmetry, then we have that
$$\...
0
votes
0answers
29 views
How to find the flux integral if the vector field is given in cylindrical coordinates?
I'm given the following vector field equation which is in cylindrical form:
$$\vec{D} = \rho^4 \hat{\rho}$$
I want to find the flux through the surface of two cylinders which are both centered at the ...
1
vote
1answer
50 views
Going from cartesian to cylindrical coordinates - how to handle division with $0$
I have three point charges with the cartesian coordinates:
$q_1(a,0,0) \: \: \: q_2(0,a,0) \: \: \: q_3(0,0,a) $,
I want to convert these into both cylindrical and spherical coordinates.
The cartesian ...
0
votes
1answer
86 views
Find an equation in rectangular coordinates for the surface represented by the cylindrical equation
The given is $$r=6\sin(\theta)$$
Multiplying both sides by $r$ yields
$$r^2=6r\sin(\theta)$$
It follows such that
$$r^2=6y$$
$$x^2+y^2=6y$$
$$x^2+y^2-6y=0$$
Completing the square
$$x^2+y^2-6y+36-36=0$$...
1
vote
1answer
25 views
Volume Above Half a Circunference and Below a Decentered Cone
So I have to compute the following integral:
$$
\iint_D \sqrt{(x-1)^2+y^2}\,dx\,dy
$$
where $D=\{(x,y)\enspace :\enspace x^2 +y^2 \le 1; \enspace y\ge 0 \}$
So, as stated on the title, this is ...
0
votes
1answer
112 views
what is a vector dot del in cylindrical coordinates? $\vec{U}\cdot \nabla$
what should be the product of :
$\vec{U}\cdot \nabla$ in a cylindrical coordinate ? for example with a scalar following the product such as $(\vec{U}\cdot \nabla) \Omega$ ? Thank you
