Questions tagged [vector-calculus]
Questions on dealing with vector calculus functions of Mathematica such as Grad, Div, Curl, Laplacian and their representations in various coordinate systems.
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Why won't this magnetic field plot?
I have been having some longstanding trouble in getting a 2D vector plot of a magnetic field to show up. For context, I am working with Lienard-Wiechert potentials and as such trying to plot the curl ...
- 13
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1
answer
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PlotLegends` and VectorAnalysis is now obsolete on Mathematica v 12.0.0.0 Home edition [closed]
My code was working a few months ago. Now I receive the messages:
...
- 175
3
votes
2
answers
93
views
Eigenvalues and classification of critical points [closed]
I started with a function (x,y) and tried to write the code to work out the eigenvalues and classify the critical points.
The output it all good up until I try to use Which[] to classify the critical ...
- 31
2
votes
1
answer
75
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Differentiating unit tangent vector does not work
I am new to Mathematica and I want to visualize the tangent and normal vector field of a particular embedding of the circle. In my code it is [CapitalGamma][s]. When I put the unit tangent vector (uT[...
- 35
1
vote
1
answer
71
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Plotting the electric field of the Lienard-Wiechert potentials
I am having a very rough time trying to properly define and then vectorplot the expression for the electric field of the Lienard-Wiechert potentials I have been trying to code. Up to this point, the ...
- 13
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66
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How to get $ (\vec{A} \cdot \nabla) \vec{b}) $ to evaluate in Wolfram language [duplicate]
I am quite new to Wolfram language, and I am trying to use it to prove the equality $$ \nabla (A \cdot B) = A \times (\nabla \times B) + B \times (\nabla \times A) + (A \cdot \nabla)B + (B \cdot \...
1
vote
2
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Map water runoff flows near Ellicott City, Maryland
Ellicott City, Maryland was the site of a flash flood several years ago due to the local topography. How can we use the Wolfram Language to show the direction water flows at many points near that city?...
- 594
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votes
2
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359
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How are Symbolic Vectors Defined?
It is my understanding that undefined symbols are considered scalars, so I can't index variables that aren't defined.
It is possible to define a symbol as a vector of symbols as follows, allowing ...
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0
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How do I prevent, or get rid of the <code>Abs^\[Prime]</code> in the output of a partial of a Normalize[vector]? 12.0.0 for Microsoft Windows [duplicate]
12.0.0 for Microsoft Windows
How do I prevent, or get rid of the Abs^[Prime] in the output of a partial of a Normalize[vector]?
The code below shows the problematic ...
- 1,447
1
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1
answer
58
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'not a variable' error when applying D function [closed]
I am trying to apply differentiation, D, operator in Mathematica to a vector. Importantly, I want to carry out the operation with respect to another vector. Basically, I am computing a Jacobian matrix....
- 33
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51
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Polar to Cartesian coordinate transformations [duplicate]
I'm trying to plot the energy boundary function EBminus[r, \theta, LL, S, BB] using Polar to Cartesian coordinate transformations. The plot should be a closed curve....
- 87
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0
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Vector Potential Function of Vector Field with DSolve?
(This is a redux of this.)
Why doesn't this work? I have a vector field F1 whose div is 0 with a known vector potential function A2, and I try to get DSolve to solve the differential equation for A2 ...
- 263
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132
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Find Vector Potential from Vector Field with Div = 0?
This works to compute the scalar potential function of a vector field whose curl is 0 (using the DifferentialForms.m package):
...
- 263
2
votes
1
answer
113
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Preventing Mathematica from applying product rule
I am programming viscous terms of compressible Navier-Stokes equations
...
- 33
1
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2
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116
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Showing each component of velocity in a helix
In this animation, I want to show each component of velocity (V_x, V_y and V_z) with arrows ...
- 1,502
2
votes
1
answer
59
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Simplifying expressions with dot or non-commutative product (without the help of NCAlgebra)
I have two expressions (with dot and non-commutative product):
$f=J^T.x+J.x$
$g=J^T**x+J**x$
I want to simplify them and get the following expressions:
$f=(J^T+J).x$
$g=(J^T+J)**x$
In an attempt to ...
- 2,344
1
vote
2
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Calculating Matrix Derivatives
I'm sorry if this is an easy question, but I'm trying to refresh my memory on calculating derivatives of matrix products and have been reading the Matrix Cookbook. I'd like to rebuild my intuition by ...
- 185
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0
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How to define a vector operator?
I know how to define a single-variable differential operator like
Clear[Op]
Op[x_] := a D[#, {x, 1}] &
and I can do operations like
...
- 189
3
votes
5
answers
848
views
Calculating length of curve based on data points?
I had around $1000$ data points $(x,y,z)$ and when I plot them they seem to lie on a closed curve. I carefully checked the data points and the points do not repeat rather they are somewhat close to ...
- 199
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votes
1
answer
136
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Why isn't the vector field being plotted over the entire torus?
I am trying to plot a vector field over a torus. Here is my code and the image it produces:
...
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2
votes
1
answer
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Solving a vector diferential equation lead to ComplexInfinity Encountered non-numerical value for a derivative at t == 0
I'm trying to solve the following Vector PDE:
I implemented the following code:
...
- 673
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0
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106
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Implementing the 3D Radon transform
I am wondering how to implement the Radon transform, the 3D Radon transform, that is, given a 'density' function $f: \mathbb{R}^3\to \mathbb{R}$ The Radon transform of $f$ is $$Rf(s,w)= \int_{x\cdot w=...
- 109
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Using `GradientFilter[]` and `GradientOrientationFilter[]` to reproduce Matlab's `gradient()` function
In 'gradient' function in MMA, two methods are given to reproduce Matlab's gradient() function. I thought that ...
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58
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How to express elemental operations in matrix form?
I ran the following code:
X = Array[x, {5, 4}];
W = Array[w, {4, 3}];
Y = Array[y, {5, 3}];
D[Norm[X.W-Y, "Frobenius"]^2, {W}]//MatrixForm
However, mma ...
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0
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52
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How to input a specific three-variable function into this definition?
I have the following expression:
...
- 101
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0
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47
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Looking to compute $e^{\phi}\Delta^2 f e^{-\phi}$ in a coordinate-free way
Let $f, \phi:\mathbb{R}^n\to\mathbb{R}$ with $\phi(x)$ looking like $\phi(x)=(x+a)^2$ for some $a\in\mathbb{R}^n$. I am interested in computing $$L_\phi(f)=e^{\phi}\Delta^2 \left(e^{-\phi}\,f\right)$$ ...
- 101
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58
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Calculation of SolidAngle not recognizing region?
Basically I'm trying to calculate the solid angle of a square seen from the origin. I defined the region (in two different ways) and tried running the function but it does not give any output.
Why is ...
- 58
3
votes
2
answers
124
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Solving an integral vectorial equation by iterations
I'm triying to solve a problem like the following:
$$
\binom{f(t)}{g(t)}=\binom{f_0(t)}{g_0(t)}+\lambda\int_0^t ds\hat{A}(s)\binom{f(s)}{g(s)},
$$
where $f_0(t),g_0(t)$ and $\hat{A}(t)$ (a $2\times2$ ...
- 491
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45
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Output of expressions unable to have operations be performed on the expression
I am currently trying to use the code linked in the catalog of spacetimes pdf to calculate chirstoffel symbols for a metric which follows as
n := 4
...
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0
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61
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Algorithm: Permutations & Signature
Theoretical side
Simple example: If I have two sets $A_1=\{1,3\} ,A_2=\{2,3\}$
and Permutations[{1, 2, 3}]= $\left(
\begin{array}{ccc}
1 & 2 & 3 \\
1 &...
- 732
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1
answer
80
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Derivative of quadratic form in NCAlgebra
I installed the NCAlgebra package in the hope that it contains enough rules for symbolic work with most branch-matrix expressions.
...
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2
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1
answer
134
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Inactive form for PDE and symmetry
I would like to solve the following non-linear Poisson equation (as a toy problem for a more complicated problem)
...
3
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2
answers
150
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Set of quadratic forms and linear algebra
I have a set of quadratic forms.
$L_{1}=u_1^TJ_{1}u_1$
$L_{2}=u_2^TJ_{2}u_2$
$L_{3}=u_3^TJ_{3}u_3$
where $u_{i=1,2,3}$ - 3$\times$1 vector;
where $J_{i=1,2,3}$ - 3$\times$3 matrix;
I need to pack ...
- 2,344
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votes
1
answer
207
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How do I find the unit vector in the direction of the minimal rate of change?
A ball falls on the surface $x^4 z+x^9 y^2+y^2 z^3=65$ at the point (-1,-3,2). How do I find a three-dimensional unit vector in the direction that the ball will begin to roll. I know that the ball ...
- 115
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1
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147
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How to compute the divergence of a four-vector?
I have a quadri-vector which is given by
u = {(E^(-φ0[r]))*(1 - ε δφ[t,
r]), (E^(-φ0[r])) D[ε ξ[t, r], t], 0,
0}
and a quantity n which is given by
<...
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0
answers
61
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Difference in covariant derivative and divergence?
defining polar Minkowski metric (with indecies down in polar coordinates) as
gdd = {{-1, 0, 0, 0},{0, 1, 0, 0},{0, 0, r^2, 0},{0, 0, 0, r^2 Sin[\[Theta]]^2}}
...
- 612
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votes
1
answer
82
views
Finding the Curvature of the path of a particle
How do I find the curvature of the vector when t=5?
The function is:
v[t_] := {2 t^4 + 2, 6 t^3 + 1, 3 t^2 + 4}
- 115
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1
answer
269
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The square of Abs of a complex number
We all know that
4^2 + 22^2 = 500
Is there a natural way to generates 500 from the complex number ...
- 4,037
3
votes
1
answer
226
views
Pattern matching with two variables - derivatives on 4-vectors
I am interested in pattern matching with two variables and not just one, and more specifically implementing derivatives on 4-vectors. In the case of interest the 4-vectors have two indices; one is in ...
- 4,226
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votes
2
answers
94
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How to deduce cosine theorem with vector?
I want to prove the cosine theorem of triangles with vectors under the following assumptions:
...
- 1,921
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86
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How would you write a electric field in cylindrical coordinates?
I am new to Mathematica and I am trying to automate the process of finding electric and magnetic fields for TE and TM modes in a cylindrical superconducting cavity. I could not find documentation ...
1
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1
answer
76
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find a scalar potential function f for F so that f(0,0)=1
I need to find a scalar potential function f for F so that f(0,0)=1.
a force field F(x,y) = <-Sinx,-2Cosy>
First prove F is conservative
Curl[F[x, y], {x, y}]
...
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79
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Is it possible to generate a random vector space in Mathematica?
The idea is that I’d like to try to use Mathematica to work through proofs. So if a proof says, “Let there be a vector space V…”, I would like to see a concrete representation of that vector space in ...
- 101
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3
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151
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Drawing circles on top of a vector field drawn using VectorPlot
I am using the command
VectorPlot[{{y, -x}}, {x, -4, 4}, {y, -4, 4}]
to plot the vector field $\vec{V}=y\hat{i}-x\hat{j}$. On top of this, I need to draw circles ...
- 167
2
votes
1
answer
244
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Symbolic Vector calculus
Can mathematica perform symbolic vector calculus? Say I want to find
$$\mathbf{v} = \mathbf{a} \exp(\mathbf{b}\cdot\mathbf{x})$$
$$\nabla \cdot \mathbf{v} = \mathbf{b}\cdot \mathbf{v}$$
If I try
...
- 21
2
votes
1
answer
212
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Using Curl and Grad in cylindrical coordinates gives different result than in Cartesian
I am doing a quite elementary calculation to verify
$$
\vec \nabla\cdot V = \vec\nabla \times \vec A
$$
Where $V$ is just some scalar function in $\rho$, $\phi$ and $z$ and $A$ is defined as
$$
...
0
votes
1
answer
128
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How to stack several vector plots using StreamPlot?
I would like to plot several stream plots as is in ref/StreamPlot (Mathematica 12).
As is reported in the section: Generate a list of stream plots of varying [Lambda]:
I did not change but it does not ...
- 545
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votes
0
answers
57
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High-dimensional second-order differential matrix equations
I am working on Lagrangian derived high-dimensional motion equations for a robot in matrix form. The structure of such an equation is known:
$M(q)\ddot{q}+C(q,\dot{q})\dot{q}+G(q)=0$
where $q=[\dot{\...
- 2,344
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506
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Derivative matrix by vector in Mathematica
This is an excerpt from the article https://www.sciencedirect.com/science/article/abs/pii/S0094114X10000418.
How do I write this using vector-matrix operations (...
- 2,344
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1
answer
104
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Derivative of Kronecker product by vector in Mathematica
I'm struggling with the following problem. It is necessary to find the derivative expression with respect to the vector $u$:
$r(u,v)=[(u-v)(u-v)^T]\begin{pmatrix}
1\\
1\\
1
\end{pmatrix}=[(u-v)\otimes ...
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