Questions on polar coordinates, a coordinate system where points are represented by their distance from the origin ($r$) and the angle the line joining the point and the origin makes with the positive horizontal axis ($\theta$).

learn more… | top users | synonyms

1
vote
0answers
80 views

Curl in cylindrical coordinates

I'm trying to figure out how to calculate curl ($\nabla \times \vec{V}^{\,}$) when the velocity vector is represented in cylindrical coordinates. The way I thought I would do it is by calculating: ...
0
votes
2answers
95 views

Dirac delta from polar coordinates to cartesian coordinates

I have: $$k_x = k \cos\theta\\k_y=k\sin\theta$$ I would like to rewrite in terms of $k_x$ and $k_y$: $$\exp(in\theta)\,\frac{\delta(k-\alpha)}{k}$$ I start from: ...
1
vote
2answers
93 views

$f(x,y)=\langle y- \cos y, x \sin y\rangle$

$f(x,y)=\langle y-\cos y,x\sin y\rangle$ $C$ is the circle $(x-3)^2 + (y+4)^2 = 4$ orientated clockwise. Relevant theorems: Green's theorem (this is under the Green's theorem section of our book). ...
3
votes
2answers
1k views

Dirac delta in polar coordinates

Given $$x=r\,\cos\theta\\y=r\,\sin\theta$$ and $$x'=r'\,\cos\theta'\\y'=r'\,\sin\theta'$$ how can I express $$\delta(x'-x)\delta(y'-y)$$ in terms of the polar coordinates? And the more general ...
5
votes
2answers
2k views

Plotting in the Complex Plane

I just wonder how do you plot a function on the complex plane? For example,$$f(z)=\left|\dfrac{1}{z}\right|$$ What is the difference plotting this function in the complex plane or real plane?
4
votes
1answer
66 views

Polar coordinations - problem with r and $\theta$

let's take a look on Archimedean spiral. the polar equation is $r = \theta$. click here to look. but $\tan (\theta) = y/x$ and $r = \sqrt{x^2+y^2}$, so $r = \theta \rightarrow \tan(\sqrt{x^2+y^2}) ...
0
votes
1answer
34 views

Determining the correct upper bound for an integral in polar coordinates

This seems super easy. But i am just a little bit stuck here. Haven't done much calculus recently. Can someone help me out real quick? Thank you in advance!
4
votes
2answers
346 views

Integration of radial functions?

Let $f(|x|)$ be a integrable radial function in $\mathbb{R}^n$ ($|\cdot|$ denotes the euclidean norm as in convention). The following identity is used to simplify computations ...
1
vote
1answer
130 views

How did theta become equal to 3pi/4 here?

How did theta become equal to 3π/4 in this particular example? Find a set of polar coordinates (r,θ) of the cartesian point (-4,4) such that -2π ≤ θ ≤ 2π and a. r > 0 and θ > 0 b. ...
1
vote
1answer
147 views

Inaccuracy in numerical calculation of arclength of part of an ellipse

I am trying to numerically calculate the arclength of part of an ellipse according to: $$ L = \int_0^{\phi_s}\sqrt{r^2+\left(\frac{dr}{d\phi}\right)^2} d\phi $$ where $r$ is defined as: $$ ...
1
vote
1answer
617 views

Finding area between two polar curves using double integrals

I have a homework question that is asking me to find the area that lies: Inside the curve $r=2+cos(2\theta)$ But outside the curve $r=2+sin(\theta)$ I think I'm supposed to be using a double ...
4
votes
3answers
344 views

Trying to understand the meaning of symmetry

The picture below is the solution to the following problem as presented in my book: Find the area of the region that lies inside both curves $$r = 8 + \cos \theta \\r = 8 − \cos θ$$ According to ...
1
vote
1answer
160 views

Moment of inertia of a circle

A wire has the shape of the circle $x^2+y^2=a^2$. Determine the moment of inertia about a diameter if the density at $(x,y)$ is $|x|+|y|$ Thank you
4
votes
1answer
202 views

Mexican Hat wavelet in polar coordinates

I'm interested in wavelet framework for polar coordinates. In the paper of Hou&Qin (2012) was proposed a general method for definition of MH wavelets on a certain manifold. In short, first we ...
2
votes
2answers
171 views

Find Cartesian equation of $r=\theta$

I solved this problem, but I'm not sure my answer is correct as it seems very complex (compared to the polar equation). Did I make some mistake along the way or is it the right solution? $$r=\theta$$ ...
0
votes
2answers
2k views

Don't understand how to use jacobian for transformation of coordinates

Hello. I fail to understand why the Jacobian matrix is used to transform Cartesian coordinates to polar coordinates. If I'm not misunderstanding, it is assumed that the matrix ...
2
votes
1answer
2k views

Find a Cartesian equation of $r = 4\cos\theta$

I was able to figure the substitutions inside the equation, but I'm stuck with the equation's manipulation that will give me the solution. What would be my next step? $$r = 4\cos\theta$$ $$r^2 = ...
4
votes
2answers
200 views

Parametrization of a curve in polar coordinates

I'm trying to change this parametrics equations to polar coordinates $$ X(t) = 2\cos(t) - \sin(2t) \\ Y(t) = 2\sin(t) - \cos(2t) $$ What i tryed to do was raise the two equations squared, sum ...
2
votes
1answer
101 views

Line integral of $F = r \times k$ on hemisphere

Exam revision - Verify Stokes theorem directly by explicit calculation of the surface and line integrals for the hemisphere $r=c$, with $z \geq 0$, where $F = r \times k$ and $k$ is the unit vector ...
1
vote
1answer
163 views

Polar Coordinates: Dividing by the variable “r.”

Evaluate the iterated integral by converting to polar coordinates: $\large \int^2_0 \int^{\sqrt{2x-x^2}}_0 xy~dy~dx$ I successfully completed most of the problem; however, I had difficulty ...
0
votes
1answer
426 views

How does one interpolate between polar coordinates?

I'm finding that when I try to use the standard methods of interpolation in polar space, the result is not what I would expect. For example, when interpolating between the following polar coordinates: ...
0
votes
2answers
292 views

Finding the centroid of a polar curve

The curve is $r = e^{-b\theta}$ where $b > 0$ and $θ \in [0, \infty)$. I got that the arc length is $\frac{\sqrt{b^2 + 1}}{b}$ (is this correct?), but computing the centroid $(x, y)$ looks awful. ...
3
votes
1answer
806 views

How to calculate the area between 2 polar curves: $r=\frac{4}{2}-\sin\theta$ and $r=3\sin\theta$?

How to calculate the area between 2 polar curves: $r=2-\sin\theta$ and $r=3\sin\theta$? I know that one curve is a limaçon and the other is a circle. I have them drawn out as well, my only question ...
1
vote
2answers
80 views

Integration, polar coordinates

My question is general rather than specific.If a problem requires to find the area of a figure bounded by a curve given in polar coordinates,how do we find the limits of integration analytically ...
3
votes
1answer
74 views

polar coordinates ..question about the answer from the solution manual

Im trying to figure out but for some reason I dont know how to...could someone please tell me how did they get this answer from the solution manual....they skipped steps so I have no idea
1
vote
1answer
116 views

Express in Rectangular Form

a) $(-1+i)^{-i}$ so I know that the answer is $9.92-3.58i$. My track getting there is off. I know that $x=-1$ and $y=1$, so $r = \sqrt{2}$, also that $\displaystyle \theta=-\frac{pi}{4}$. I've ...
2
votes
0answers
33 views

Pure differential equation whose solution is a siluroid?

I am trying to find a differential equation for the siluroid that DOES NOT contain explicitly $\theta$, $\sin\theta$, or $\cos\theta$, but only $\rho$, $\dot\rho$, $\ddot\rho$. The siluroid equation ...
0
votes
0answers
203 views

Polar Fourier transform in Matlab

I have a 2D signal: sg=sin(x+y). To represent it in 2D I use meshgrid: [xx,yy]=meshgrid(x,y) and I plotted it with ...
2
votes
4answers
419 views

Converting x^2 + 6y - 9 = 0 to polar

Hi I'm trying to solve this problem but am having difficulty removing the remaining r. I have tried http://i.imgur.com/iJk9b2g.jpg but cannot get an answer Any help is appreciated
1
vote
1answer
79 views

Polar coordinate

Let $f(x,y)$ be a differntiable function in $\mathbb{R}^2$ so that $f_x(x,y)y=f_y(x,y)x$ for all $(x,y)\in\mathbb{R}^2$. Find $g(r)$ so that $g(\sqrt{x^2+y^2})=f(x,y)$ and $g$ is differentiable in ...
2
votes
1answer
122 views

evaluation of double order integral using polar co-ordinates

When evaluating double integral using polar co-ordinates, does the order of $dr ~ d\theta$ make any difference? Suppose, $$\int_0^{\pi/4}\int_0^{\sin\theta} r^2 dr d\theta$$ ...
1
vote
1answer
112 views

How to calculate a double integral over a triangle by transforming to polair coordinates & by using a transformation

Let T be the triangel with vetrices $( 0,0 ) , ( 1,0 )\mbox{ and } ( 0,1 ) $. Evaluate the integral : $$ \iint_D e^{\frac{y-x}{y+x}} $$ a) by transforming to polar coordinates b) by using the ...
1
vote
1answer
159 views

triple integral - ecliptic coordinate

I need to find the $V$ by triple integral. the limits from up is (1) - ecliptic cone. and from dwon - (2) - elepsoide. $$(1) \ \ \ \ z=-\sqrt{3x^2+5y^2}$$ $$(2) \ \ \ \ {3 \over 10}x^2+5y^2+{z^2 ...
1
vote
0answers
170 views

gradient of an axis symmetric vector field in cylindical coordiantes

I am trying to calculate with a general approach the gradient of an axis symmetric vector field in cylindrical coordinates and then express it in cartesian coordinates. First I write my vector ...
1
vote
2answers
4k views

Find the area of the Rose's petal.

If a Rose leaf is described by the equation $r = \sin 3\theta$, find the area of one petal.
0
votes
2answers
24 views

Polar coordinates that uses $\frac { 1 }{ Z_1 }$

I am doing polar coordinates, and I am stuck when my book asks to do $\frac { 1 }{ Z_1 }$. I have no problems with $\frac { Z_1 }{ Z_2 }$ and $Z_1Z_2$. Here is the values for $Z_1$ I'm not so much ...
1
vote
1answer
135 views

What happens to a line in polar coordinates when orgin is moved and rotated in cartesian coordinates?

Let's say we have an Archimedean spiral in Cartesian coordinates. This corresponds to a line in polar system (i.e. $r=a\theta+b$). Now if I move the origin of the Cartesian coordinates system to ...
1
vote
2answers
118 views

Coordinate system conversion: what it is called what I'm doing?

I want to do a simple coordinate transformation and would like to know what is the rigorous way to describe this mathematically in order to be able to search for algorithms for more complex ...
0
votes
1answer
61 views

Polar form $\frac{dy}{dx}$

Trying to find the derivative $\dfrac{dy}{dx}$ in polar form, where: $$x=r\cos\theta \,\text{ and } \, y=r\sin\theta$$ Seems like the common approach (on Wikipedia and other sites) is to assume that ...
0
votes
2answers
93 views

What is the inverse $z^{-1}(z)$ of $z(\varphi)=e^{i\varphi}$ with $\varphi\in\Bbb N_0$?

Suppose I am given a complex number $z=x+iy\in\Bbb C$, with $\left|z\right|=1$, and I am told that $z=e^{i\varphi}$ for some integer $\varphi\in\Bbb N_0$ (the value of which is not given to me). How ...
2
votes
1answer
9k views

Ellipse in polar coordinates

I think Wikipedia's polar coordinate elliptical equation isn't correct. Here is my explanation: Imagine constants $a$ and $b$ in this format - Where $2a$ is the total height of the ellipse and $2b$ ...
0
votes
0answers
86 views

How to solve following non-linear differential equation?

Let's have an equation $$ \left(\frac{\partial f}{\partial r}\right)^{2} + \frac{1}{r^{2}}\left(\frac{\partial f}{\partial \varphi}\right)^{2} = g(r). $$ How to solve it?
0
votes
1answer
55 views

Qualitative analysis of an ordinary differential equation in polar coordinates

I want to draw the integral curves of the differential equation in polar coordinates $(\theta, \rho)$ $\frac{d\rho}{d\theta}= \rho^3-6\rho^2+8\rho$ At first I thought it would suffice to analyse ...
2
votes
1answer
139 views

Really Stuck on Partial derivatives question

Ok so im really stuck on a question. It goes: Consider $$u(x,y) = xy \frac {x^2-y^2}{x^2+y^2} $$ for $(x,y)$ $ \neq $ $(0,0)$ and $u(0,0) = 0$. calculate $\frac{\partial u} {\partial x} (x,y)$ and ...
1
vote
1answer
73 views

Polar coordinates parameters

Sketch in the same diagram the curves with polar equations $r=2a\cos\theta$ and $2r(1+\cos\theta)=3a$ and find the polar coordinates of their points of intersection. What is the polar equation of ...
1
vote
3answers
127 views

Converting $x^2 + 6y - 9 = 0$ to polar.

So far I got here \begin{align} (r\cos\phi)^2 & + 6 r \sin\phi- 9 = 0\\ (r\cos\phi)^2 & = 9 - 6r \sin\phi \end{align}
2
votes
1answer
119 views

Converting polar to cartesian?

So far I got \begin{align} r & = 7 / (4 - 2 \cos\theta) \\ r (4 & - 2\cos\theta) = 7 \\ r (4 & - 2( x / r ) ) = 7 \end{align} I apologize in advance for the bad formatting.
2
votes
2answers
779 views

Convert $ x^2 - y^2 -2x = 0$ to polar?

So far I got $$r^2(\cos^2{\phi} - \sin^2{\phi}) -2 r\cos{\phi} = 0$$ $$r^2 \cos{(2\phi)} -2 r \cos{\phi} = 0$$
1
vote
1answer
467 views

Double integral area : how to find the curve equation

I have the following equation $$(x+y)^{4} = ax^{2}y$$ I need to find the area limited by the equation above. I know I have to transform x and y in polar coordinates: $$\begin{align*} &x = ...
0
votes
3answers
135 views

Cartesian and Polar Coordinate

I should give the Cartesian Coordinates $(x,y)\in \mathbb{R\times R}$ and Polar Coordinates $(r,\varphi)\in R^+\times [0,2\pi)$ of the following Complex Numbers: a) $z_{1}=-i$ b) $z_{2}=\sqrt{3}+i$ ...