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 ...
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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: ...
Brendan Darrer's user avatar
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 ...
noodles's user avatar
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2 votes
1 answer
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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[...
Ama's user avatar
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1 answer
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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 ...
JDRobin's user avatar
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66 views

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 \...
noobiewannabe's user avatar
1 vote
2 answers
224 views

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?...
Ted Ersek's user avatar
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4 votes
2 answers
359 views

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 ...
NullPointerException's user avatar
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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 ...
Steven Thomas Hatton's user avatar
1 vote
1 answer
58 views

'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....
dylewiczk's user avatar
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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....
MMS's user avatar
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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 ...
Jeffrey Rolland's user avatar
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132 views

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): ...
Jeffrey Rolland's user avatar
2 votes
1 answer
113 views

Preventing Mathematica from applying product rule

I am programming viscous terms of compressible Navier-Stokes equations ...
dylewiczk's user avatar
1 vote
2 answers
116 views

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 ...
user84456's user avatar
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2 votes
1 answer
59 views

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 ...
dtn's user avatar
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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 ...
HonestMath's user avatar
1 vote
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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 ...
z.v.'s user avatar
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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 ...
BAYMAX's user avatar
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3 votes
1 answer
136 views

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: ...
valcofadden's user avatar
2 votes
1 answer
64 views

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: ...
Joshua Salazar's user avatar
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106 views

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=...
NotaChoice's user avatar
1 vote
0 answers
47 views

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 ...
ZachB's user avatar
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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 ...
ADEric's user avatar
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How to input a specific three-variable function into this definition?

I have the following expression: ...
Dispersion's user avatar
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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 $$L_\phi(f)=e^{\phi}\Delta^2 \left(e^{-\phi}\,f\right)$$ ...
Dispersion's user avatar
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58 views

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 ...
Claudio Mora's user avatar
3 votes
2 answers
124 views

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 $2\times2$ ...
Jorge Castaño's user avatar
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45 views

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 ...
aygx's user avatar
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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 &...
Emad kareem's user avatar
1 vote
1 answer
80 views

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. ...
dtn's user avatar
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2 votes
1 answer
134 views

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) ...
Thela Hun Ginjeet's user avatar
3 votes
2 answers
150 views

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 ...
dtn's user avatar
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1 answer
207 views

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 ...
Arnold's user avatar
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1 vote
1 answer
147 views

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 <...
Isabella Nunes's user avatar
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61 views

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}} ...
Nitaa a's user avatar
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0 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}
Arnold's user avatar
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1 vote
1 answer
269 views

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 ...
imida k's user avatar
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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 ...
a_User_with_No_namE's user avatar
2 votes
2 answers
94 views

How to deduce cosine theorem with vector?

I want to prove the cosine theorem of triangles with vectors under the following assumptions: ...
lotus2019's user avatar
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0 votes
0 answers
86 views

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 ...
Aarav Mande's user avatar
1 vote
1 answer
76 views

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}] ...
calcNoob1's user avatar
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79 views

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 ...
hmltn's user avatar
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1 vote
3 answers
151 views

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 ...
Solidification's user avatar
2 votes
1 answer
244 views

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 ...
Lucas Gruwez's user avatar
2 votes
1 answer
212 views

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 $$ ...
Willem Govaerts's user avatar
0 votes
1 answer
128 views

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 ...
irondonio's user avatar
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57 views

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{\...
dtn's user avatar
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0 votes
1 answer
506 views

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 (...
dtn's user avatar
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0 votes
1 answer
104 views

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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