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

0
votes
1answer
25 views

Arc length of polar curve

I was trying to determine the arc length of the polar curve $r = f(\theta) = a(1 - \cos \theta)$, and it was going well until I got to the definite integral. I know that $f'(\theta) = a \sin \theta$, ...
1
vote
1answer
19 views

2D finite difference boundary conditions for radial direction

I am trying to solve Poisson's equation in an axisymmetric cylindrical domain using finite difference. So I start with my differential equation and boundary conditions and discretize them. However, ...
0
votes
2answers
408 views

converting kph and heading to xyz velocity vector

I am writing software (in C++) that is required to send out messages from our simulation system to another simulation system. Problem is we track the simulation object's current speed (kph) and ...
0
votes
0answers
9 views

polar moment of area for nonplaner circle (cup)

Can somebody tell me the polar moment of area of chord for a sphere. for example when you cut a sphere at a point other than from center? Also polar moment of area for curved axis symmetry ?
0
votes
3answers
450 views

Find the cube roots of $ -8 i $ and plot them on a plane.

I can’t figure out the angle of this equation. I set it up like this: $$ z^{3} = 0 - 8 i. $$ I find that the $ r $-value is $ 2 $, but when I try to find the angle, I’m stuck. I can’t divide by $ 0 ...
0
votes
0answers
13 views

Integrate in cylindrical coordinates

$\vec{\nabla} p = \rho \vec{f}$ How do you solve this in polar coordinates? I can't find a way to insert g in my equation. I would have to split it in $r$ and $\phi$. So $y=sin(\phi) * r$ but I ...
1
vote
0answers
79 views

Convert geodetic coordinates to cartesian coordinates

I am working on some simulation software that will represent a number of entities in a defined geographic area in the world. The part of the software that I am currently working on is to implement ...
1
vote
1answer
50 views

Find centre of mass of a circle when one half is heavier than the other half?

I have a problem which simply states: Consider a circle (lamina) of radius 1 with centre (0,0) where the left half is twice as heavy as the right. Find its centre of mass. Extend your solution to ...
2
votes
1answer
37 views

How can $r$ be negative when dealing with polar coordinates?

If by definition $r=\sqrt{x^2 + y^2}$, then why do we allow $r$ to be negative? Relatedly, I do not understand the last section of this conversation discussing points being represented by multiple ...
1
vote
1answer
25 views

Integral: Area of figure described in polar coordinates

Lets say we have a figure described as follows: $r=2\cdot\sqrt{\cos(2\theta)}$ Click here to see a plot. Now lets say that we want to calculate the area of this rotated eight. I'd like to ...
0
votes
1answer
85 views

Getting coordinate between two coordinates knowing the distance and latitude

That is my wall: I know the coordinates of the lower points (left and right). (X1,Y1,Z) and (X2,Y2,Z) where X is the latitude, Y longitude and Z the altitude. I want to know the another point of ...
0
votes
0answers
28 views

Triple Integration: from Cartesian to Polar Coordinates

I have to evaluate $\iiint_Q (x+y)^2 dV $, where $Q$ is a solid hemisphere within the bounds $z \ge 0$, $\space x^2+y^2+z^2 \le 4$. I am assuming that in order to solve the above integral I have to ...
-1
votes
0answers
21 views

Rewriting Integral Forms

I am asked to (1) Rewrite the integral $ \iint \limits _R f(x,y) \space \Bbb dx \Bbb dy$ in different coordinates $u,v$. (2) Hence, derive the form the integral $\iint \limits _R f(x,y) \space \Bbb ...
6
votes
2answers
2k views

Finding a point on Archimedean Spiral by its path length

I've been curious about Archimedean Spirals and their relations to Sacks Spirals and prime numbers. I would like to draw some visualizations of the points with a given distance from the center, ...
1
vote
1answer
33 views

Area calculation

How could we best approach calculating the area inside $r=\cos^{2n-1}(x)+\sin(x)$, $0\leq x\leq \pi$, for $n=1,2,...$? For $n=3$ we get the following "potato/bean" graph: and for $n=51$ we get ...
0
votes
3answers
48 views

What is the first step I should take in solving this equation?

I have to change this polar equation and put it in terms of $x$ and $y$. $$r = \frac{5}{5\cos(\theta) + 6\sin(\theta)}$$ I was guessing that I should multiply all the terms by r and then convert ...
2
votes
2answers
47 views

Graphing polar equation $r\sin \theta = 1$?

How would you graph $r \sin \theta = 1$? I know that $r\sin \theta$ is equal to $y$, but the place where I'm told to graph this function on is a polar graph. How should I go about this?
0
votes
0answers
25 views

The gradient in $n$-dimensional spherical coordinates

I am in the middle of a computation where I need to work with the formula of the gradient in spherical coordinates in $\Bbb R ^n$ (no preferred convention for the angles). I could patiently and ...
0
votes
1answer
13 views

Identical transformation about integrals

\begin{align} I &=\int_0^1dr\int_0^{2\pi}\left(cos\theta\cdot\frac{\partial f}{\partial x}+sin\theta\cdot\frac{\partial f}{\partial ...
1
vote
4answers
37 views

convert rectangular coordinate (-3,0) to polar coordinate

I'm trying to convert (-3,0) to polar coordinate. I can get r=$\sqrt {(-3)^2 +(0)^2}$ =3, but when computing for the angle $\theta$=$\tan^{-1} (\frac {0}{-3})$=0 but the answer for the ...
1
vote
1answer
26 views

Equations of Motion in Polar Basis

A particle of mass m moves under a central force field $ \mathbf{F}=-k\mathbf{r}$ where k is a constant with dimensions $ N m^{-1} $. Assuming that the particle moves in the equatorial plane ( ...
0
votes
1answer
25 views

Region bounded by a Polar Curve

For a National Board Exam: Find the area of the region bounded by a polar curve $r^2 = a^2 \cos(2\theta)$ Answer = $a^2$. So I cheated a bit and plotted the curve on wolfram so i could ...
0
votes
2answers
18 views

Area inside a curve and outside a Cardoid

For a National Board Exam: Find the area which is inside the curve r=3cos(theta) and outside the cardoid r=1+cos(theta) Answer is pi Ok I am trying to setup the right definite integral for ...
0
votes
1answer
23 views

Area enclosed by polar curves

Given $$r_1(\theta)=2(1+\cos\theta) \\ r_2(\theta)=2(1-\cos\theta)$$ I want to find the area of the region resulting from the intersection of those curves. Is the following integral correct? $$ 2A= ...
0
votes
1answer
430 views

Conversion of a complex number into polar form

Below is the complex number that is to be converted into Polar form. I'm facing problem in second part of this number(after + mark not the (b) itself). When I divide them(10/-5+j12) directly, by ...
4
votes
2answers
63 views

From Gravity Equation-of-Motion to General Solution in Polar Coordinates

I'm having trouble getting the general solution of this differential equation. The gravitational equation of motion is, for constants $M$ and $G$ and position vector $\vec{r}$, $$\frac{d^2}{d ...
-4
votes
1answer
60 views

Express -i in polar exponential form

Express $-i$ in form $r\cdot e^{i\cdot \theta}$ $r=1$ is simple enough. As on an Argand diagram, $-i$ will be at $(0,-1)$. Does $\theta = 3\pi/2$ here? Or -$\pi/2$ to get it $-\pi < \theta < ...
4
votes
1answer
34 views

Square inside a Polar coordinate system

I have a square lying on a polar coordinate. Is there any general relationship between radius and angle, which may be derived along the side of square. More generally put, given the coordinates of the ...
1
vote
0answers
19 views

Diffusion equation in polar coordinates with non-zero boundary conditions (BC)

I'm trying to solve the diffusion equation in polar coordinates: $$c_t = \frac{D}{r^2}[2r\,c_r + r^2\,c_{rr}] = \frac{D}{r}[2\,c_r + r\,c_{rr}] \tag{1}$$ with the following BC: $$c(0,t)=0, \quad ...
-1
votes
0answers
38 views

polar coordinate transformation

If we have an equation $\mathcal{L_I}=\prod \mathrm{exp}\bigg(-\lambda_j \displaystyle\sum\limits_{m=1}^{\Psi_{j}}\binom{\Psi_j}{m} ...
0
votes
2answers
45 views

Find the maximum radius for given theta and phi (spherical coordinates) that will fall within a cuboidal boundary

I have a cuboid with measurements (width, depth, height) which is my boundary. The origin is the center of the cuboid. Given a theta(Azimuth) and phi(elevation), how do I find the highest radius that ...
0
votes
1answer
420 views

How to find the limits of integration to get the area for a loop of a lemniscate?

I know how to integrate the squared radius to get the equation that'll give me the area, like such for a lemniscate with $r^2=8\sin(2\theta)$ : $$1/2\int 8sin(2\theta) = 4 \int \sin(2\theta) = 4 * ...
0
votes
1answer
36 views

Line segment equation in polar coordinates

I have a line segment given by two points $A$ and $B$. $$A+u(B-A), u\in[0,1]$$ when doing calculations with this segment, it would be advantageous to have it written in polar coordinates around some ...
1
vote
0answers
413 views

Polar Integration over intersection of two circles

Let $C_0$ denote a circle centered at $(0,0)$ with a radius of $r_0$ and let $C_1$ denote a circle of radius $r_1$ centered at a point $(x_1,0)$. Assume that we are given some function, $\phi(r)$ ...
1
vote
1answer
15 views

Finding the horizontal and vertical tangents of a parametric equation.

Find the points at which the polar curve $r=2+2\sin{(\theta)}$ has a horizontal or vertical tangent line. Translate the parametric equation to Cartesian coordinates: $$ r^2=2r+2r\sin{(\theta)} ...
1
vote
1answer
330 views

How to prove that the graph of $r=\sin\left(\frac{\theta}{2}\right)$ is symmetric about polar axis

I want to know how to prove that the graph of $r=\sin(\frac{\theta}{2})$ is symmetric about the $x$-axis (polar axis). As I understand it, if a polar graph is symmetrical about the $x$-axis, ...
0
votes
1answer
20 views

Polar conversions of coordinates and parametric equations

Express the polar coordinates $P\left(6, -\dfrac{\pi}{4} \right)$ in Cartesian coordinates. $\displaystyle x=r\cos{(\theta)} ,\ y=r\sin{(\theta)} \implies x^2+y^2=r^2 \wedge \theta = ...
2
votes
3answers
21 views

Eliminate the parameter of a

Eliminate the parameter to find a description of the following circles or circular arcs in terms of $x$ and $y$. Give the center and radius, and indicate the positive orientation. ...
1
vote
1answer
63 views

Find the area using double integral and polar coordinates.

I need to find the area using double integral and polar coordinates. $$y=3-x$$ $$y^2=4x$$ This is what i figured already: $${r\cos{\theta}+r\sin{\theta}} = 3$$ $$r=0, r=3, \theta=0, \theta=\pi/2$$ ...
1
vote
0answers
23 views

Converting cartesian to polar integral

I feel like I almost have a grasp on regions of integration, I am a bit frustrated that I haven't fully gotten it but because I feel like I'm almost there. In this particular homework problem I have a ...
0
votes
2answers
16 views

Setup region of integration for polar coordinates

I've been working on a homework set for Calc III, right now we're emphasizing double integration and polar integrals. I keep having problems conceptualizing where to actually create my region of ...
1
vote
1answer
32 views

Equation to place points equidistantly on an Archimedian Spiral using arc-length

I am looking for a way to place points equidistantly along an Archimedes spiral according to arch-length (or an approximation) given the following parameters: Max Radius, Fixed distance between the ...
1
vote
1answer
53 views

Is this a valid example of a non-euclidean Sierpinski attractor?

I am learning the basic concepts about the Chaos Game (I did a previous question about the same topic here), the method to create fractals elaborated by professor Michael Barnsley. The basic example ...
5
votes
4answers
140 views

Adding two polar vectors

Is there a way of adding two vectors in polar form without first having to convert them to cartesian or complex form?
2
votes
2answers
37 views

Volume of a cube in spherical polars

Let us calculate the volume of the cube using spherical coordinates. The cube has side-length $a$, and we will centre it on the origin of the coordinates. Denote elevation angle by $\theta$, and the ...
0
votes
1answer
45 views

Is it a good way to find polar equations of curves?

When I was in my first year of Prepa classes it was not at the program but we have to see it on an example and our maths teacher did it with hypocycloïd and epicycloïd too for fun, well it was very ...
3
votes
5answers
7k views

Polar equation of a circle

A very long time ago in algebra/trig class we did polar equation of a circle where $r = 2a\cos\theta + 2b\sin\theta$ Now I forgot how to derive this. So I tried using the standard form of a circle. ...
0
votes
1answer
12 views

Perpendicular distance from a 3D point to a vector in spherical polar coordinates.

I have a point $(r, \theta, \phi)$ and a direction vector with angles $(\theta', \phi')$. What would be the method to calculate the shortest distance from the point to the vector?
0
votes
0answers
45 views

Vector Calculus - Polar Co-ords

I am having a lot of difficulty finding an approach to solving the following question: A dyon is a particle with both electric and magnetic charge; in suitable units $$\mathbf{E} = ...
1
vote
1answer
57 views

Polar equation for a Heptagon [duplicate]

What is polar equation of a Heptagon ? I need to move some Android views in the form of a heptagon, for I need to have polar equations for Heptagon like for $x= r\sin(\theta)$ and $y=r\cos(\theta)$. ...