0
votes
1answer
16 views

Help understanding polar coordinates and conversion between polar and rectangular

I'm not understand this. I understand that you can take normal functions with x's and y's and convert them into polar coordinates. I also understand that the polar form of that function will have the ...
0
votes
1answer
14 views

Find a vector in cartesian coordinates given its relative location to another vector in spherical coordinates

Here is my problem: -I have an arbitrary normalized vector N in cartesian coordinates -I am trying to find normalized vector M, also in cartesian coordinates -I am given the azimuth and polar ...
0
votes
2answers
44 views

Show that the four points given below are the vertices of a rhombus.

Show that the four points, $(5, 8), (7, 5), (3, 5)$ and $(5, 2)$ are the vertices of a rhombus. I tried solving it, by finding out the distances by using the formula $\sqrt{(x_{2}-x_{1})^2 + ...
2
votes
1answer
105 views

Jacobian for a Cartesian to Polar-Coordinate Transformation

I have a simple doubt about the Jacobian and substitutions of the variables in the integral. suppose I have substituted $x=r \cos\theta$ and $y=r \sin\theta$ in an integral to go from cartesian to ...
0
votes
1answer
35 views

Representation of differentials in Polar Coordinates

We define polar coordinates in $\mathbb{R}^{n}$\ $\{ 0\}$ by $x=ry$, where $r=|x|>0$ and $y \in \partial B(0,1)$ is a point on the unit sphere. In the coordinates, Lebesgue measure has the ...
0
votes
0answers
18 views

Getting latitude/longitude from a 2d co-ord system [duplicate]

Given a latitude/longitude and a distance and bearing in relation to that point, how can I find the latitude/longitude of the new position? Distances can range from 0-100km so curvature of the earth ...
0
votes
1answer
45 views

Geometry finding area problem

A regular 2N -sided polygon of perimeter L has its vertices lying on a circle. Find the radius of the circle and the area of the polygon.
3
votes
0answers
60 views

Changing coordinate system with non standard definitions

The standard coordinate transformation to polar coordinates is $$ \begin{cases} x=r\cos(\varphi)\\ y=r\sin(\varphi) \end{cases} $$ with $r\in[0,\infty), \ \varphi\in[0,2\pi)$ The question is whether I ...
2
votes
1answer
81 views

Need a hint on what's wrong - polar coordinates

I'm asked to solve the following $$ \int^2_0 \int^\sqrt{4-y²}_0 \sqrt{4-x^2-y^2} dxdy $$ I thought about using polar coordinates: (1) $0 \le x \le \sqrt{4-y^2}$ is the upper half of a circumference ...
1
vote
2answers
264 views

How to verify a conversion to spherical coordinates?

Is it possible to verify if a conversion of an integral in Cartesian coordinates to spherical coordinates was done correctly other than revising it looking for mistakes? I mean, is there some kind of ...
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?
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 ...
1
vote
1answer
161 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
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 ...
3
votes
1answer
415 views

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, ...
0
votes
1answer
79 views

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. ...
1
vote
0answers
64 views

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 ...
1
vote
0answers
107 views

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 ...
2
votes
1answer
59 views

gradient in polar coordinate by changing gradient in Cartesian coordinate

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 ...
5
votes
2answers
117 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 ...
6
votes
4answers
3k 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 ...
2
votes
1answer
2k 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} + ...
1
vote
0answers
749 views

Conversion of motion equation from Cartesian to Polar coordinates: Is covariant differentiation necessary?

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 = ...
1
vote
1answer
143 views

Bijections of the plane

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 ...