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.
294
questions
3
votes
2
answers
171
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 ...
0
votes
0
answers
31
views
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
vote
1
answer
52
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....
- 33
0
votes
0
answers
49
views
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
1
vote
0
answers
42
views
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
0
votes
0
answers
81
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):
...
- 263
2
votes
1
answer
107
views
Preventing Mathematica from applying product rule
I am programming viscous terms of compressible Navier-Stokes equations
...
- 33
0
votes
0
answers
42
views
Determining the number of steps it takes to reach the minimum of a function starting at some initial point
I think I understand the idea. I have my function, the global minimum of that function, the point I am going to start at, and the step size. Here is my code below:
...
1
vote
2
answers
103
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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 ...
- 1,094
2
votes
1
answer
54
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 ...
- 2,304
1
vote
2
answers
123
views
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
1
vote
0
answers
65
views
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
774
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
3
votes
1
answer
114
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:
...
- 155
2
votes
1
answer
59
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:
...
- 623
0
votes
0
answers
86
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 $$Rf(s,w)= \int_{x\cdot w=...
- 109
1
vote
0
answers
43
views
Using `GradientFilter[]` and `GradientOrientationFilter[]` to reproduce Matlab's `gradient()` function
In 'gradient' function in MMA, two methods are given to reproduce Matlab's gradient() function. I thought that ...
- 1,168
0
votes
0
answers
55
views
How to express elemental operations in matrix form?
I ran the following code:
X = Array[x, {5, 4}];
W = Array[w, {4, 3}];
Y = Array[y, {5, 3}];
D[Norm[X.W-Y, "Frobenius"]^2, {W}]//MatrixForm
However, mma ...
- 1
0
votes
0
answers
52
views
How to input a specific three-variable function into this definition?
I have the following expression:
...
- 101
0
votes
0
answers
47
views
Looking to compute $e^{\phi}\Delta^2 f e^{-\phi}$ in a coordinate-free way
Let $f, \phi:\mathbb{R}^n\to\mathbb{R}$ with $\phi(x)$ looking like $\phi(x)=(x+a)^2$ for some $a\in\mathbb{R}^n$. I am interested in computing $$L_\phi(f)=e^{\phi}\Delta^2 \left(e^{-\phi}\,f\right)$$ ...
- 101
0
votes
0
answers
51
views
Calculation of SolidAngle not recognizing region?
Basically I'm trying to calculate the solid angle of a square seen from the origin. I defined the region (in two different ways) and tried running the function but it does not give any output.
Why is ...
- 58
3
votes
2
answers
117
views
Solving an integral vectorial equation by iterations
I'm triying to solve a problem like the following:
$$
\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 $2\times2$ ...
- 481
0
votes
0
answers
43
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
...
- 119
0
votes
0
answers
55
views
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 &...
- 614
1
vote
1
answer
74
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.
...
- 2,304
2
votes
1
answer
105
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)
...
3
votes
2
answers
133
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 ...
- 2,304
0
votes
1
answer
162
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 ...
- 115
1
vote
1
answer
128
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
<...
0
votes
0
answers
56
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}}
...
- 438
0
votes
1
answer
79
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
1
vote
1
answer
211
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 ...
- 3,529
3
votes
1
answer
221
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 ...
- 4,188
2
votes
2
answers
90
views
How to deduce cosine theorem with vector?
I want to prove the cosine theorem of triangles with vectors under the following assumptions:
...
- 1,719
0
votes
0
answers
71
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 ...
1
vote
1
answer
65
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}]
...
- 39
0
votes
0
answers
75
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 ...
- 101
1
vote
3
answers
90
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 of radii $1,2,3...$, etc. I am no ...
- 157
2
votes
1
answer
174
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
...
- 21
2
votes
1
answer
180
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
$$
...
0
votes
1
answer
121
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 ...
- 505
0
votes
0
answers
51
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{\...
- 2,304
0
votes
1
answer
337
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 (...
- 2,304
0
votes
1
answer
94
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 ...
- 2,304
1
vote
1
answer
149
views
Quadratic form derivative in Mathematica
How to correctly differentiate quadratic form by vector in Mathematica, i.e.:
$Q=\omega^T I_{p} \omega$
$\frac{dQ}{d\omega}= ??? $
...
- 2,304
5
votes
2
answers
616
views
'gradient' function in MMA
How to calculate Numerical gradient of 2D arrays using the "gradient function" ("Matlab-like")?
"[___] = gradient(F,hx,hy,...,hN) specifies N spacing parameters for
the ...
- 1,796
1
vote
0
answers
81
views
StreamPlot works slow with analitical functions
I'm day to day user in Mathematica, that's I will be happy to any kind of help in code optimisation.
So, I try to plot gradient for beatings between two laser modes and plot intensity, phase and phase ...
- 11
3
votes
0
answers
67
views
Excess lines in the solution plot of vector ODE [closed]
I've got an ODE system, which I attempt to solve by two ways: solving the system itself, and using vector ODE.
Here is code of first way:
...
1
vote
1
answer
357
views
how to define unit vectors in mathematica
I'm struggling a little bit trying to understand how to address this problem, I would like to do this in mathematica: is just that I don't know how to do the dot product between $\mathbf{J}$ and $\...
- 13
0
votes
1
answer
65
views
Vector function projection raises an error
Working on ODE systems solution with NDSolve[] I decided to try to replace system of equations like:
...