Questions tagged [coordinate-systems]

This tag involves questions on various coordinate systems. The usual Cartesian coordinate system can be quite difficult to use in certain situations. Some of the most common situations when Cartesian coordinates are difficult to employ involve those in which circular, cylindrical, or spherical symmetry is present. For these situations it is often more convenient to use a different coordinate system.

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Phase Space Intersecting Hyperplane - Poincare Section/Map

I have a phase space and a hyperplane. I would like to know how I can find where the coordinates intersect the hyperplane. My plan is to create a Poincare Section/Map. The problem is I have no ...
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Find the Y Coordinate of a Right-Angled Triangle Vertex Given the X and Y Coordinates of the Two Other Vertices [closed]

Please help: given the coordinates of the vertex A (11; 2) and B (3; 8) of a right-angled triangle, find the Y coordinate of C given its X coordinate is 0 (without using trigonometric functions)
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Harmonic functions and coordinate transfomation

Related to a question about coordinates, I've been given the following comment to consider: "Local coordinate functions are given by suitable harmonic functions on subsets of the metric space, ...
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Transformation of line element in Minkowski space under infinitesimal coordinate variation

I'm trying to understand the following problem: We are looking at an infinitesimal coordinate transformation $$x^\mu \rightarrow x^\mu + \epsilon u^\mu(x), \space \epsilon \rightarrow 0$$ and we are ...
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How to solve different grid based combinatorics problems?

First of all, I apologize for this post being huge. With that being said, I am practising for mathematics olympiad. I have come across different problems that I have tried to solve. Recently, I have ...
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Need help with matrix transformation! [closed]

Given the transformation = [1 −2 3, 2 0 −3, 1 1 1][x1 x2 x3] . Find the co-ordinates (x1, x2, x3) corresponding to (2,3,0) in Y.
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Common normal for an ellipse and parabola

I came across the following question in a magazine with example problems for the JEE examination in India: Given are two curves $x^2/a^2 + y^2/63=1$ and $y^2=4x$. The maximum integral value of $a$ ...
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How are 3 coordinate frames related to each other?

Suppose we have three cartesian 3D-coordinate systems, each related to each other via some Euler angles. So for instance, if we have a vector $\vec v$ and its coordinates in the first frame, we get ...
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Why do Trigonometric functions _need_ to be negative?

The Trigonometric Unit Circle is a pretty common thing taught in High-School, yet it doesn't cover some questions I had. There have been questions in the past about why trigonometric functions can be ...
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Conic sections ( coordinates of the point of intersection of tangents with the curve )

I was told by my math teacher that equation of a pair of tangents drawn from the point is $T^2=SS_1$ This gives a second degree equation in $X$ and $Y$, which represents a pair of straight lines ...
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Polar equation of a shifted cardioid?

I am trying to find the equation (in polar form) of a cardioid shifted by an amount $x_0$ in the $x$ direction. I tried converting $r=1+\cos(\theta)$ in Cartesian coordinates, add $x_0$ to the $x$ ...
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3D rectangle coordinates knowing 2 coordinates , and the elevation of the 2 others

I have this simple 3D geometry problem that I need to solve in order to go to the next step with a python script. Please check the attached image. here is what I know : A, B coordinates (X,Y, Z) A ...
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Defeated by coordinate spaces and transformations; need help figuring out what questions to ask

I'm trying to write a toy app that generates "procedural art" by rolling circles around inside each other. I have been banging my head against the math for months now, repeatedly thinking I'...
22 views

System coordinate rotation, using a vector's value [closed]

Say I have two 3d cartesian coordinate systems, with one being a rotated version of the other. And say I have a vector A, and know its coordinates in both systems, can I get the rotation that was ...
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Is it matrix vector multiplication or matrix coordinate multiplication?

Recently I got confused about the difference between a vector and a coordinate and here is what I concluded. Given a vector space $V$ over a field $F$, a vector in the vector space $\vec{w}$ and a ...
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3D points backprojected onto a 2D plane.

In a Cartesian 3D coordinate system defined by XYZ, there is a known point $\textbf{P}$ defined with it coordinates $(x_0, y_0, z_0)$ in X-Y plane. Following is the diagram: $P$ in X-Y plane is ...
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Rigorously defining coordinate systems on physical space

I just started reading about manifolds and learned of coordinate charts. I am trying to mentally piece together my intuitional understanding of coordinates in our physical space (PS) vs the definition ...