Questions tagged [coordinate-transformation]

Questions relating changing coordinate systems of numerical points and analytical expression including vector fields and vector analysis.

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3
votes
2answers
238 views

Plot eigenfunctions w/ looped boundary conditions on a torus

How we can show results (eigenfunctions) obtained in this post on the surface of a torus, not on a square? https://www.wolfram.com/language/11/differential-eigensystems/investigate-a-laplace-equation-...
0
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1answer
44 views

Transformation of Differential Operators

I would like to gain some knowledge about how to transform differential operators to different coordinate systems using Mathematica. I know that the Laplacian ...
7
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3answers
241 views

Tensor transformation

Consider the following tensor in coordinate basis $T=T^{\mu}_{\nu\lambda} \partial_{\mu}\otimes dx^\nu \otimes dx^\lambda$ in two dimensions with coordinates $x^1 = x$ and $x^2 = y$. We take $T^{\mu}...
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2answers
117 views

Converting a Spherical Polar vector to Cartesian [closed]

I have the vector: $$sin2\theta(cos\phi +\frac 1 2sin\phi)\vec r +2cos2\theta(cos\phi+\frac 1 2sin\phi)\vec \theta +2cos\phi(\frac 1 2cos\phi -sin\phi)\vec \phi$$ in spherical polar coordinates which ...
2
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2answers
64 views

EulerMatrix with axes other than X, Y an Z

The Mathematica function EulerMatrix[{Alpha, Beta, Gamma},{a,b,c}] gives the Euler matrix for rotation about X, Y and Z axes. Here by choosing the order of a, b and ...
0
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1answer
51 views

Changing the dependent variable

I'm using NDSolve to solve a set of ordinary differential equations. The output is something like. ...
2
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1answer
195 views

How can I plot the gradient field in bipolar coordinates?

how I can plot the gradient of function V according to the attached program in bipolar coordinates. I used from ParametricPlot to show bipolar coordinates as: ...
2
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1answer
31 views

ImageForwardTransformation always puts origin at lower left

I am trying to create a notebook which will graphically display the effect of simple geometric maps, for the purpose of teaching linear algebra. Here is what I thought would work. I created an image ...
0
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1answer
37 views

Affine transform of sparse list (x,y,z) to a region of x^2 + y^2 + z^2 = 1.0

I have list of x,y,z points (somewhat random) that leads to the image shown below: I am trying to map this data to essentially a sphere shape using an affine transform. My original attempt was to ...
0
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0answers
29 views

How to automate the transformation into spherical coordinates of a region

I've this region: S = { (x,y,z) ∈ R^3 | 2 * Sqrt[x^2+y^2] <= z <= 1 + x^2 + y^2} Now I would like to transform the coordinates into spherical ones, so as to ...
1
vote
1answer
53 views

Coordinate transform of discrete data

let's say I have a set of discrete data of dimension n by n by n, which may represent a scalar field $f(x,y,z), x,y,z\in [-1/2,1/2]$ in Cartesian 3D space. To be specific, ...
2
votes
2answers
83 views

Computational efficient way to find a SL(2,Z) matrix between two set of vectors [closed]

Suppose I have two sets of vectors (let's say it 2d, but it would be nice to generalize it to arbitrary dimensions): $(v_1,v_2,\ldots,v_n)$ and $(v'_1,v'_2,\ldots,v'_n)$ and they have integer entries, ...
0
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0answers
32 views

Help with a custom coordinate transformation

I'm just starting to use Mathematica and can't wrap my head around the task I have at hand. It comes from field-theory. (Sorry I had to insert formulas as images instead of proper LaTex as it would ...
4
votes
1answer
106 views

Convert partial differential equation (Fokker-Planck equation) from polar to cartesian coordinates

I am trying to convert the following equation in polar form to the cartesian coordinates using Mathematica (Phys. Rev. A 78, 013810 (2008), https://journals.aps.org/pra/abstract/10.1103/PhysRevA.78....
0
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1answer
105 views

Transformation in Mathematica (Dilation, Reflection, Translation)

Is there a Mathematica command which allows us to do various translations on a function (dilation, reflection, translation)? For example, consider f[x_] = x^3. Hoe ...
0
votes
1answer
55 views

Making change of variable

I have the following expression $$L=\frac{m}{2}\left(\dot{q}^{2} \sin ^{2} A t+\dot{q} q A \sin (2A t)+q^{2} A^{2}\right)$$ with $q=q(t)$ I want to make a change of variabl $$Q=q\sin(At)$$ By hand I ...
0
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0answers
59 views

Transformation of coordinates in Mathematica

I would like to know how I can transfer the coordinate system origin in the attached object to the centroid (Red points) and then change all the points coordinates relative to the new origin. (i.e....
4
votes
3answers
165 views

Is there an intuitive and rational way to automatically convert ranges into coordinates?

I'm tired of typing and deciphering coordinates of the corners rectangles, and I'm wondering if anyone has found a better way. A rectangle can simply be described by two lists ...
1
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0answers
47 views

Axial Symmetric 2D Cylindrical Field to Cartesian 3D Field

Previously, I've used 2-dimensioned [radius, zeta] output from NDSolve ({InterpolatingFunction, InterpolatingFunction}] and used the FieldTransform to convert the axial-symmetric cylindrical slice to ...
7
votes
2answers
399 views

Cylindrical coordinates in FEM

I am trying to solve the Stokes equation for fluid flow in a 3d cylinder. All boundaries are no-slip, apart from the top boundary, which enforces flow in the x-direction. My problem is that I can't ...
0
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0answers
90 views

Convective derivative in cylindrical coordinate

My question is similar to this one about convective derivative. But how do I adapt it to the cylindrical coordinate? Simply changing Grad to cylindrical coordinate ...
0
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0answers
20 views

How to impose periodicity conditions on some variables?

I have a quantity ds2 which is expressed in term of a set of 5 variables (let's call them t, r, θ, φ, ψ). I have 5 equations (...
0
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1answer
42 views

Re-Expressing Quantity Using Different Set of Variables

I have a quantity ds2 which is expressed in term of a set of 5 variables (let's call them t, r, θ, φ, ψ). I have 5 equations (...
1
vote
1answer
43 views

Get coordinates of points after `Translate[]`

Suppose I have some small set of points Pts in 3D space: ...
1
vote
1answer
79 views

SchurDecomposition doesn't work (in a weird way)

I have written a function to get the canonical form of a 3D quadric surface. This involves finding a unitary transformation of the coordinates which eliminates the cross-terms such as $xy$ or $xz$. ...
3
votes
1answer
144 views

Difficulties on Mathematica code to solve Christoffel Symbols of a particular metric

I) The Problem There's a particular metric $[1],[2]$ in general relativity which is written as: $$ds^{2} = -[c^2-v_{s}^2f(r_{s})^2]dt^2+v_{s}f(r_{s})dtdx+v_{s}f(r_{s})dxdt+ dy^2+dz^2 \tag{1}$$ So ...
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3answers
500 views

How to calculate the divergence of stress matrix in polar coordinate system correctly

I calculate the divergence of stress matrix in polar coordinate system by the method of coordinate transformation as follows : ...
1
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0answers
25 views

Set coordinates system for the notebook

Is there a way to set the coordinates system globally, for the whole notebook? Back in earlier versions, there was SetCoordinates[] from the Vector Analysis package... I would like to be able to set ...
2
votes
1answer
76 views

Plotting cartesian coordinate data point in spherical coordinate

I have field value in cartisian coordinate i.e. {x,y,z,Ex,Ey,Ez}= {{-6.1935, 0.1505, -6.4695, 41186.7, 68876.6, -8859.19}, {-5.5125, 0.1505, -6.4695, 3914.28,...
0
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0answers
38 views

How to get the transformation function from one plane to another?

Suppose I have a plane which passes through some point $(x_0,y_0,z_0)$ and has a (normalized) surface normal $n$. Consider as an example a plane that passes through the point ...
2
votes
1answer
281 views

How to solve for Transpose[X] A X = B

I need to find a transformation matrix of the metric tensor but I don't know how to solve for X from Transpose[X]*A*X=B
2
votes
1answer
71 views

Cannot remove ragged edges of TransformedRegion plot

I am working with two mappings of a region in the complex plane and I can't eliminate the ragged edges of the region in the second map and do not see anyway to add points to make the perimeter smooth ...
0
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3answers
54 views

Point manipulations to list form

I tend to do a lot of code the manual way, which doesn't work out for bigger data sets. I wanted to know if there were in built functions to do the following; ...
1
vote
1answer
101 views

Plot in Physical Space? [closed]

...
1
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1answer
62 views

Polynomial transformation coefficients

Given a 3D polynomial of degree $m$ and coefficients $a_{ijk}^0$, $$p(x_0, y_0, x_0) = \sum_{i,j,k}^{m} a_{ijk}^0 x_0^i y_0^j z_0^k, \quad i + j + k \le m,$$ I want to make the transformation: $$x_0 =...
1
vote
0answers
30 views

Coordinate transformation of a table of multi-variable function values

I've created a table in Mathematica for a function dependent on r and phi of the form ...
5
votes
2answers
267 views

How do I get actual values from a Jacobian matrix?

I have a Jacobian function: D[{Sqrt[x^2 + y^2], ArcTan[x, y]}, {{x, y}}] It gives me a matrix with the formulas I need for my transposition matrix: ...
0
votes
0answers
81 views

Distance matrix inside a neural net

So what I would like to do is to create a NetGraph that takes in an $n\times 3$ (with $n$ varying in length) list of 3D coordinates as an input and creates an $n \times n$ distance matrix or an $\frac{...
2
votes
1answer
87 views

Hammer projection to rectangular

This might be more of a mathematical problem than a Mathematica'l one, but still, maybe you'd help me. I want to write a function that would produce a rectangular image from an image with Hammer ...
3
votes
1answer
109 views

Convert a point in the Radon Space to a line

I need a function point2line to convert a point in the Radon Transform Space to a straight line. But I don't know the algorithm inside mathematica, I don't know ...
10
votes
5answers
2k views

Polar contour plot in Mathematica?

I am following a text on fluid mechanics with MAPLE examples. I want to do the following ContourPlot in Mathematica in Polar coordinates: $$ (r^2-\frac{a^3}{r}) \...
1
vote
1answer
55 views

Error with StateSpaceTransform: the rule based transformation must be of length 2

I would like to perform a change of variables on the following dynamics system: ...
0
votes
0answers
57 views

General coordinate transfomation

I am looking for a (free) package or snippet that makes the transformation of tensors between spacetimes easy. What do you suggest?
1
vote
1answer
80 views

Plot Using User-defined Coordinates

Suppose instead of using Cartesian coordinate $\vec{x}=(1, 0)$ and $\vec{y}=(0, 1)$, I want to define new coordiates $\vec{a} = (1,0)$ and $\vec{b} = (\frac{1}{2},\frac{\sqrt{3}}{2} )$. And when I ...
3
votes
2answers
175 views

Does Laplacian use first argument “theta” for polar angle or azimuthal angle?

Only example I could find in the help for Laplacian is this My question is, is $\theta$ meant to be the polar or the azimuthal angle? Using $\theta$ for polar is ...
2
votes
2answers
187 views

Converting from UPS(x, y) to geodetic latitude/longitude

I'm trying to create a program which converts latitude/longitude (wgs84) to UPS (Universal Polar stereographic) coordinates, and then UPS(x, y) to WGS 84. I mean Given UPS(x, y), be able to compute ...
3
votes
2answers
131 views

ArrayPlot in polar coordinates?

I have a 2-D array ($360 \times 512$). The 360 rows represents the azimuthal angle from (0° to 359°) and the 512 columns are radial segments. This is the ArrayPlot...
3
votes
1answer
128 views

Where to find order of arguments for default functions

Lets take for example the Laplacian. So I want to apply it in spherical coordinates, so I go the the associated documentation page (https://reference.wolfram.com/language/ref/Laplacian.html?view=all) ...
9
votes
3answers
269 views

Error in TransformedField

I am using TransformedField to convert a system of ODEs from Cartesian to polar coordinates: ...
0
votes
2answers
131 views

VectorDensityPlot, [closed]

I'm trying to plot the following function for two different values of variable m. However, it seems the second figure never appears. Weirdly, I noticed that real numbers are being attributed to ...