# Tagged Questions

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### Why aren't polar coordinates global?

Using polar coordinates, why cant we use one coordinate neighbourhood to cover $\mathbb{R}^2$? Can't every point in $\mathbb{R}^2$ can be described by its distance from the origin and its angle from ...
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### Solid angle subtended in latitude-longitude maps

I need to scale a latitude-longitude map with the solid-angle each "pixel" subtend. How can I obtain the said solid angle starting from the $\phi$ and $\theta$ angles? Thank you very much
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### Radians : negative and positive values

Recently I have been reading books on DSP where I came across Polar co-ordinates. I understand that on Polar graph (4 quadrants) we have 0,pi/2,pi,3/2pi and 2pi radians as we move from one quadrant to ...
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### What distinguishes elliptical coordinates from polar coordinates?

I am trying to identify what characteristic distinguishes elliptical coordinates from polar coordinates. For concreteness, let's write down the expressions. Polar: $$x=r \cos(t) \\ y=r \sin(t)$$ ...
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### How many kinds of simple coordinates are there in a 2D space?

The question comes form an idea to solve a motion-with-potential problem in 1D space by finding a mathematically equivalent uniform-motion problem in 2D space. ...
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### Converting from set of Cartesian equations to Polar Equation

Is it possible to convert the set of Cartesian equations: $$x(t) = (20-30)*\cos(2t)+45*\cos(2t*(20-30)/20))$$ $$y(t) = (20-30)*\sin(2t)+45*\sin(2t*(20-30)/20))$$ where $$t \in [0,2\pi)$$ Into a ...
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### Convert $r^2\cos(2\theta)=9$ to Cartesian

I need to convert $r^2\cos(2\theta)=9$ to Cartesian coordinates. How should I do it? What I did: $$r^{2}\cos2\theta=r^{2}2\cos^{2}\theta-1=9\Rightarrow r^{2}\cos^{2}\theta=5\Rightarrow x^{2}=5$$ Did ...
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### 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 ...
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### 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 ...
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### Computing gradient in cylindrical polar coordinates using metric?

I am trying to understand coordinate transformations properly (having studied some general relativity in the past). Let us consider the transformation from cartesian to cylindrical coordinates, ...
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### Getting coordinate between two coordinates knowing the distance and latitude

That is my wall: http://imageshack.us/f/266/wall2z.png/ I know the coordinates of the lower points (left and right). (X1,Y1,Z) and (X2,Y2,Z) where X es the latitude, Y longitude and Z the altitude. ...
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### Knowing coordinates of a point having two coordinates and the distance.

I have the two geographic coordinates of the lower corners of a wall. So, for example, i want to know what is the coordinate that is for example 15cm on the right of the lower corner left. Is that ...
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### Circle-Circle intersection coordinate system

Consider two points in the 2D Euclidean plane, the origin $0$ and $x$. One can define a co-ordinate system such that for any point $y$ in the plane, $y$ is parametrized by its distance from $0$, call ...
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I'm tried to do following and I can't see what went wrong. $$\begin{bmatrix} \hat r\\ \hat \theta \end{bmatrix} = \begin{bmatrix} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta ... 2answers 123 views ### Why does it always take n numbers to characterize a point in n-dimensional space (or does it)? I don't know if this is obvious and a dumb question or not, but, here we go. To characterize a point in 2-d space we can use standard x,y coordinates or we can use polar coordinates. There are ... 4answers 4k views ### Simple proof of integration in polar coordinates? In every example I saw of integration in polar coordinates the Jacobian determinant is used, not that i have a problem with the Jacobian, but I wondered if there's a simpler way to show this which ... 1answer 3k views ### Transforming the Laplace operator from Polar to Cartesian coordinates I'm trying to find the error in my logic here. Let's say we are given the Laplace operator in polar coordinates:$$ \frac{\partial^2}{\partial r^2} + \frac{1}{r}\frac{\partial}{\partial r} + ...
Say I have the following equation of motion in the Cartesian coordinate system for a typical mass spring damper system: M \; \ddot{x} + C \; \dot{x} + K \; x = ...
I recently had to deal with polar coordinates and thus wondered: "Polar coordinates" is just a special name for some bijection from $\mathbb{R}^2$ to $\mathbb{R}^2$ that can be very easily visualized ...