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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Spherical Polar Coordinates VectorPlot3D

I understand the VectorPlot3D function allows you to plot a 3D vector ${Vx,Vy,Vz}$ as a function of $x,y,z$. Is there a function that allows you to plot in ...
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-2 votes
1 answer
91 views

help me to clarify the transformation of the functions by using Mathematica

help me to clarify the transformation of the functions by using Mathematica
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3 votes
2 answers
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Plotting a family of 2D curves of a surface of revolution using spherical coordinates

I am trying to plot the family of curves $V = constant$ from the following surface of revolution expressed in spherical coordinates $(r,\theta,\phi)$ with $\phi = constant$:$$ V = \frac{2 r\sin\theta}...
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How to project a 2D region from one plane to another?

I have one of a general set of 2D regions (Disk, Rectangle, Polygon, etc.), as well as 3D origin points and normal vectors defining two reference planes/coordinate systems. I want to find a series of ...
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How to convert a PDE from cartesian to spherical coordinates?

I am investigating solutions to $\Delta u - x\cdot \nabla u=0$ in $\mathbb{R}^n$ and I would like to convert this equation from cartesian to spherical coordinates in mathematica. How should I go about ...
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Looking to compute $e^{\phi}\Delta^2 f e^{-\phi}$ in a coordinate-free way

Let $f, \phi:\mathbb{R}^n\to\mathbb{R}$ with $\phi(x)$ looking like $\phi(x)=(x+a)^2$ for some $a\in\mathbb{R}^n$. I am interested in computing $$L_\phi(f)=e^{\phi}\Delta^2 \left(e^{-\phi}\,f\right)$$ ...
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  • 101
3 votes
1 answer
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Help converting Cartesian to Spherical Symbolically [closed]

I am attempting to use Mathematica for basic coordinate conversion symbolically but I am struggling to get it working. In the example below I am trying to convert from cartesian to spherical. Any help ...
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-1 votes
1 answer
140 views

Solution this problem to illustrate the conformal mapping [duplicate]

Find the mapping of circle using confirmal mapping ( joukowski tansformation method) Assume w= z+1/z 〖z=re〗^iθ = 〖r(cosθ+isinθ)〗^1 ( a Circle with radius r and center (0,0))
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2 votes
2 answers
192 views

Coordinate Transformation

I'm trying to define a module (in Mathematica) that receives a point $\mathbf{p}(\mathbf{x})\in\mathbb{R}^n$ (expressed in the coordinate system $\mathbf{x}$) and a coordinate transformation $\bar{\...
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Deconvolution To Solve For Radial Dirac Delta Expression By Laplacian, Division and Inverse Fourier?

An answer to the question "Laplacian and DiracDelta" (about a radial DiracDelta) involves taking the Laplacian of a ...
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1 answer
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Please help me insert this example into Mathematica to illustrate the transformation

Please help me insert this example into Mathematica to illustrate the transformation
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Sorting Cartesian coordinates

Here is the problem: I create a coordinate list as follows: ...
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1 vote
1 answer
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Does have Mathematica a built-in function for write Dirac delta in spherical coordinate?

It has been appeared $\delta(\mathbf r_1 -\mathbf r_2)$ in one of my integrals which I have to calculate. The differentials of the integral are $dr_1d\theta_1d\phi_1 dr_2d\theta_2d\phi_2$ So I need to ...
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Finding transformation matrix for a coordinate transform

I have a matrix in two different bases. Suppose they are called $g_{\mu \nu}$ in one basis and $\eta_{ab}$ in the other basis. If the transformation between the bases is represented by $T_{\mu}^{\text{...
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1 vote
2 answers
101 views

Add gaussian noise to 2D Point

I implemented a program for a camera calibration in Mathematica with with prototypical data to see if my calibration works. Here I converted 3D object coordinates into 2D sensor coordinates. I have ...
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1 answer
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How to plot a function $\Psi (r, \theta, 0) $ and its **rot** in polar coordinates? [closed]

The function is: $\boldsymbol{\Psi}(\rho, \theta, 0)=-\left(2+\frac{8}{\rho}\right) \operatorname{Sin} \theta \boldsymbol{e}_{\boldsymbol{\theta}}+\left(2 \rho-\frac{8}{\rho}\right) \operatorname{Cos} ...
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1 answer
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Converting system of ODE from polar to rectangular coordinates

I am trying to convert the following system of equations from polar coordinates to rectangular coordinates. (A,phi)->(u,v) ...
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2 votes
1 answer
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How to find a transformation matrix between two set of operators?

The following set of operators $P_1,P_2,P_3,P_4$ and $Q_1,Q_2,Q_3,Q_4$ are related as $P_i=\sum_j w_{ij} Q_j$. How can I find the matrix $W=[w_{ij}]$? ...
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1 vote
1 answer
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How to represent polar coordinates in a easy way?

I've been using the TI-NSpire CX Cas calculator to solve some electronic problems that work a lot with polar coordinates, in this calculator representing these exercises is very easy, as shown below. ...
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4 votes
1 answer
125 views

TransformedField on Tensor

I was trying to use the TransformedField function to Transform the Metric Tensor $ds^2 = dx^2 + dy^2 + dz^2$ into Spherical coordinates. So i use: ...
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0 votes
1 answer
163 views

How to form Rigid Body Transformation Matrices?

We have two line segments specified by a pair of points $(b_1,t_1)$, and $(b_2,t_2)$. We want to find the transformation between the two line segments. Define a unit vector $z_1$ from $b_1$ and ...
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2 answers
479 views

On orthographic projection

Writing: ...
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Different results from polar and cartesian forms of a function?

I am trying to write up and study the given function: by the following Mathematica input (with N=5 and not infinity) ...
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  • 269
3 votes
1 answer
100 views

Find centre of spiral similarity of two lines

I am trying to find a formula for the centre of spiral similarity (see here) of two lines, lineAB and lineCD. My problem comes ...
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1 vote
0 answers
54 views

How to troubleshoot TransformedField functionality in Mathematica?

I list up this method to transform a complex function to Cartestian form, which can be used on virtually any function: such as: ...
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  • 269
2 votes
4 answers
222 views

Coordinate transformation can this be done with AffineTransform?

Looking for alternatives or improvements for accomplishing the following: Given the position of points A, B, and C in both the x-y and u-v planes, determine transformation functions to map values ...
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  • 977
3 votes
2 answers
276 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-...
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0 votes
1 answer
102 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 ...
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  • 841
7 votes
3 answers
477 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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  • 225
1 vote
2 answers
271 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 ...
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2 votes
2 answers
109 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 ...
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1 answer
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Changing the dependent variable

I'm using NDSolve to solve a set of ordinary differential equations. The output is something like. ...
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2 votes
1 answer
258 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: ...
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2 votes
1 answer
51 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 ...
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0 votes
1 answer
44 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 ...
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1 vote
1 answer
71 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, ...
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2 votes
2 answers
134 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, ...
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4 votes
1 answer
260 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....
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0 votes
1 answer
160 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 ...
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0 votes
1 answer
83 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 ...
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0 answers
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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....
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4 votes
3 answers
179 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 ...
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1 vote
0 answers
59 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 ...
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7 votes
2 answers
900 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 ...
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0 votes
0 answers
183 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 ...
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0 votes
1 answer
49 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 (...
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1 vote
1 answer
74 views

Get coordinates of points after `Translate[]`

Suppose I have some small set of points Pts in 3D space: ...
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  • 1,563
2 votes
1 answer
85 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 $xz$. ...
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  • 791
3 votes
1 answer
595 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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  • 483
-5 votes
3 answers
789 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 : ...
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