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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Transforming normals into a specific coordinate system
Let's say I have normals defined from points of latitude and longitude on a sphere (represents the satellite object). The coordinate system we want to transform these normals into is z points to ...
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Is there any two-coordinate system where X, Y is the same point as Y, X? [closed]
Is there any two-coordinate system where e.g., (10,36) is the same point as (36,10)?
You see we here at the Rescue Centre are at our wits' end. Half our reports come in with latitude first, half with ...
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Find the value of the interior angles of a polygon [closed]
I have coordinates of points $(x, y)$. By connecting these points we get a polygon in which I have to get values of its internal angles.
For example points = $[3,1], [3,3], [1,3], [3,5], [7,5], [7,1]$
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Number of parameters needed to find a point on $S^n$
Firstly, let me point out that the following argument can be easily extended to $S^n$ for every natural number $n$, so I will just focus on $S^1$. Consider the circumference $x^2+y^2=1$, centred at $O=...
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Equation of line passing (1,4) having minimum sum of intercept on positive axis?
We have to find Equation of straight line passing through $(1,4)$ having minimum sum of intercept on positive axis?
So I have two approaches:
Method 1
First $a+b$ ($a$ and $b$ are intercept on ...
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Sierpinski Gasket coordinate description
I was reading Gerald Edgar's "Measure, Topology, and Fractal Geometry" when I came across this exercise
Let coordinates $(u,v)$ be defined in the plane with origin at one corner of the ...
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Variational formulation of the vector Laplace equation in cylindrical coordinates
I want to solve the vector Laplace equation $\nabla^2 \mathbf{v}=\mathbf{f}$ in arbitrary coordinate systems using finite-elements.
The usual way to derive the variational form necessary for the ...
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How to combine the $4$-dimensions of spacetime into 1 dimension?
I have been thinking about the possibility of representing all points in a $4$-dimensional spacetime coordinate system $\mathbb{R}^{1,4}$, as points on one line $P$ (or axis of a $1$-dimensional ...
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Analytical solution to Stokes equation with cylinderical symmetry but with a curved region
Is there any way one could solve the following Stokes equation analytically in a system with cylindrical symmetry but with a curved region?
The set of equations in the cylindrical coordinate read
\...
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In a 2d coordinate plane, how can I find the position of point S given the angles to 3 known reference grid points on the x and y axis.
I need to understand how to find the position of a mobile robotic camera that is positioned in a defined grided area. I rotate the camera so that it points at 3 different grid reference points named B,...
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Linear approximation of the magnetic dipole field
Summary: using 3 angles to represent a magnetic dipole's orientation is redundant because the rotation around the $z$-axis of the dipole does not change the magnetic field, there are only 2 DOFs for ...
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Finding the coordinate of four points of imaginary intersecting lines which passes through end points of two intersecting lines
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I want to find the coordinates of the points A,B,C,D where two imaginary lines intersect each other, where this imaginary lines passes through the end points of the two lines L1 and L2, the ...
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Best Coordinate system - Lagrangian problem
In $\Bbb R^3$ consider an heavy point $P$ whose mass $m$ on a circumference $\Gamma$ of radius $R$, centered in the origin. Now consider that $\Gamma$ lives in the plane
$$\Pi = \{( x,y,z) \in \Bbb R^...
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Covariant and contravariant velocity
I'm facing the following problem in tensor calculus:
I want to calculate the velocity of a mass particle in spherical coordinates.
So I'm using the following coordinate functions for spherical ...
Hans-Friedrich Pfeiffer