Tagged Questions
0
votes
2answers
50 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 ...
0
votes
0answers
43 views
Which complex number cannot be written in polar form?
I'm really confused by this question. Is there such a number?
1
vote
1answer
108 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.
$$(1) \ \ \ \ z=-\sqrt{3x^2+5y^2}$$
$$(2) \ \ \ \ {3 \over 10}x^2+5y^2+{z^2 ...
1
vote
2answers
79 views
Coordinate system conversion: what it is called what I'm doing?
I want to do a simple coordinate transformation and would like to know what is the rigorous way to describe this mathematically in order to be able to search for algorithms for more complex ...
3
votes
1answer
216 views
Computing gradient in cylindrical polar coordinates using metric?
I am trying to understand coordinate transformations properly (having
studied some general relativity in the past).
Let us consider the transformation from cartesian to cylindrical coordinates,
...
0
votes
0answers
149 views
Convert cartesian coordinate to geography coordinate
i have a Canvas on my web where i get the position of the pixel when i draw. Example, X=1, Y=5. So, i have to project that on a real wall. I know the geography coordinate of each lower corner of the ...
0
votes
1answer
65 views
Getting coordinate between two coordinates knowing the distance and latitude
That is my wall: http://imageshack.us/f/266/wall2z.png/
I know the coordinates of the lower points (left and right). (X1,Y1,Z) and (X2,Y2,Z) where X es the latitude, Y longitude and Z the altitude.
...
1
vote
0answers
55 views
Knowing coordinates of a point having two coordinates and the distance.
I have the two geographic coordinates of the lower corners of a wall. So, for example, i want to know what is the coordinate that is for example 15cm on the right of the lower corner left.
Is that ...
0
votes
0answers
71 views
Circle-Circle intersection coordinate system
Consider two points in the 2D Euclidean plane, the origin $0$ and $x$. One can define a co-ordinate system such that for any point $y$ in the plane, $y$ is parametrized by its distance from $0$, call ...
2
votes
1answer
28 views
gradient in polar coordinate by changing gradient in Cartesian coordinate
I'm tried to do following and I can't see what went wrong.
$$\begin{bmatrix}
\hat r\\
\hat \theta
\end{bmatrix} = \begin{bmatrix}
\cos \theta & \sin \theta \\
-\sin \theta & \cos \theta
...
5
votes
2answers
101 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 ...
4
votes
3answers
2k 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
1k 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:
$$ \frac{\partial^2}{\partial r^2} + \frac{1}{r}\frac{\partial}{\partial r} + ...
1
vote
0answers
465 views
Conversion of motion equation from Cartesian to Polar coordinates: Is covariant differentiation necessary?
Say I have the following equation of motion in the Cartesian coordinate system for a typical mass spring damper system:
$$M \; \ddot{x} + C \; \dot{x} + K \; x = ...
1
vote
1answer
113 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 ...
