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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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
image
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
$$\Pi = \{( x,y,z) \in \Bbb R^...
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Covariant and contravariant velocity
I'm facing the following problem in tensor calculus:
I want to calculate the velocity of a mass particle in spherical coordinates.
So I'm using the following coordinate functions for spherical ...
Hans-Friedrich Pfeiffer
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Covariant (absolute) derivative of a vector along a curve -- compare cartesian vs. polar coordinates
BACKGROUND: Suppose $A^μ$ is a vector field and $x^μ(λ)$ is a curve in spacetime. A first guess at measuring the change in $A^μ$ along the curve might be
$$\frac{dA^μ(x(λ))}{dλ} = \frac{∂A^μ}{∂x^ν} \...
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Parametric Equation of a unit circle when the angle between $x$-axis and $y$-axis is not $90$ degrees
I know in regular Cartesian coordinates the parametric equation for a unit circle is $x=\cos(\theta)$, $y=\sin(\theta)$, and if the $x$ coordinates are stretched by an amount $a$, and the $y$ ...
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Equivalence of solutions to PDE in different coordinate systems
Wave equation in two dimensions can be solved either in Cartesian or polar coordinates. One can derive the expressions for Laplacian by putting in the coordinate transformations directly. However, ...
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Transformations of Function
Im having trouble conceptualizing why when we transform a function, we need to describe $x$ and $y$ as functions in the new coordinate system. For example with polar coordinates $x$ and $y$ are now ...
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How to obtain the pucker angles of a molecular ring?
The structure of the system is a ciclohexane whose conformational preference is describe in the following image:
The name of this conformational preference is "chair". Because it resembles ...
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