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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29
votes
4answers
20k views

Finding unit tangent, normal, and binormal vectors for a given r(t)

For my Calc III class, I need to find $T(t), N(t)$, and $B(t)$ for $t=1, 2$, and $-1$, given $r(t)=\{t,t^2,t^3\}$. I've got Mathematica, but I've never used it before and I'm not sure how to coerce ...
35
votes
3answers
28k views

How to make Jacobian automatically in Mathematica

If we have two vectors, $a$ and $b$, how can I make Jacobian matrix automatically in Mathematica? $$ a=\left( \begin{array}{c} x_1^3+2x_2^2 \\ 3x_1^4+7x_2 \end{array} \right);b=\left( \begin{array}{...
19
votes
2answers
5k views

Is it possible to do vector calculus in Mathematica?

I am trying to rearrange and manipulate some vector differential equations in Mathematica. As far as I understand you have to tell Mathematica that a variable is a vector by specifying the components ...
6
votes
2answers
2k views

How to change coordinates of a differential operator?

I'm doing a basic quantum mechanics problem and am trying to learn how to do it in Mathematica. Any help would be much appreciated. $\vec{L} = \vec{x} \times \vec{p}$ where $\vec{x}$ has components:...
13
votes
2answers
4k views

How to declare a 3D vector variable?

How can I do vector calculations without telling Mathematica the vector entries? I have very many arbitrary linear combinations in $\mathbb{R}^3$ which I want to perform some general calculations on (...
20
votes
4answers
885 views

What is the definition of Curl in Mathematica?

I have a usual mathematical background in vector and tensor calculus. I was trying to use the differential operators of Mathematica, namely Grad, ...
3
votes
4answers
767 views

Hypergeometric function with a matrix argument

I am looking for the evaluation of a Hypergeometric function with a matrix argument as for example in Koev and Edelman or as showcased in this Wikipedia article. From what I understand from ...
10
votes
1answer
41k views

Why I get the “Set::write: ”Tag Times in is Protected." error?

Why I get the error below with this code: ...
9
votes
3answers
701 views

Creating random configurations of spherocylinders or cylinders

About the setting: We have a 3D simulation box with side $l$ and our catesian coordinate system is set with its origin at the centre of the box. We have a number $N$ of spherocylinders of aspect ...
0
votes
1answer
212 views

How do you manipulate this in 2D

Use Manipulate to create an interactive plot that shows the parametrically-defined curve described by {x[t], y[t]} = {t Sin[t], t^2/15} for ...
14
votes
2answers
6k views

How do I plot a proper streamline plot, including spacings and line endings?

Mathematica includes two nice built-in tools to visualize vector fields, VectorPlot and StreamPlot. The latter is a useful tool, ...
18
votes
4answers
6k views

How do I plot the unit normal field for a surface?

The question is pretty much in the title; I'm about to teach my multivariable calculus students about orientations on surfaces, and I would like to be able to show them pictures. Any ideas?
10
votes
2answers
3k views

Singularities using VectorPlot

I am trying to plot a vector function of a fluid flow given by $\vec{V} = (\frac{-\cos(\theta)}{r^2},-\frac{\sin(\theta)}{r^2})$ I am trying to plot it in Mathematica using the command below, I ...
3
votes
1answer
2k views

Plot a function based on Derivative - Gradient field

I'm trying to plot the gradient field of a function in such a way that is possible to change it easily, only editing the function. Consider the code: ...
3
votes
1answer
278 views

SphericalPlot3D of an OblateSpheroid via coordinate transformation

This is an effort to reproduce an ellipse and a hyperbola of revolution from OblateSpheroidal coordinates with constant $\eta$ and $\theta$ . My approach consisted in getting a Coordinate ...
0
votes
1answer
185 views

Visualizing combined Vectors

I'm trying to visualize a cross-section of a finite continuous solenoid's B-Field (cylindrical coordinate equations from Wikipedia). I believe I have calculated the radial and z-axis fields, but I'm ...
4
votes
5answers
397 views

Computing the intersection area of two disks in 3D

Closely related to this question about highlighting intersection of two disks, I am trying to figure out if one can do so similarly for disks embedded in $3D$ (e.g. in a bounding box). The difference ...
5
votes
3answers
397 views

Finding surface normal for 3D region at a specific point

I would like to find the surface normal for a point on a 3D filled shape in Mathematica. I know how to calculate the normal of a parametric surface using the cross product but this method will not ...
12
votes
2answers
910 views

Creating randomly oriented planes

I would like to create randomly oriented planes. This is how I'm attempting to do that: I create a 2 random unit vectors, $\mathbf{v}_1$, and $\mathbf{v}_2$, in the $x$-$y$ plane I assume that if I ...
4
votes
1answer
881 views

Checking if an expression is equal to zero

I have 6 points in $\mathbb R^3$ as follows: ...
4
votes
1answer
103 views

Manipulations with tensors that keep so(3,1) symmetry manifest

I am doing some manipulations with tensors in curved background. There are, however, coordinates, where Lorentz symmetry is manifest. So, on one hand, I am dealing with particular coordinates and, on ...
2
votes
2answers
5k views

Finding scalar potential function [duplicate]

Consider the vector field defined by: $$\vec F(x,y)=\langle 2xy-\sin x,x^2+e^{3y}\rangle$$ We can check to see if the vector field is conservative with the following calculations: $$\begin{align*} \...
5
votes
2answers
244 views

Finding vector of same direction with smallest integer coordinates

To determine Miller Indices of crystal lattice planes I would need a stable algorithm which determines the smallest set of integer coordinates of a vector which has same direction as a given vector (e....
4
votes
1answer
194 views

Using Vector Operations In Mathematica

I would like to calculate $$ \mathbf T = (\mathbf B \bullet \nabla) \mathbf B$$ Where nabla (the upside down triangle) is the grad operator $(\partial/\partial x,\partial/\partial y,\partial/\...
3
votes
4answers
1k views

How to obtain the gradient of a function as a function?

The Grad function allows me to get the gradient of a function like this: ...
3
votes
2answers
133 views

Why is TensorExpand so slow for vector operations?

I would like to expand the following tensor expression: ...
2
votes
0answers
131 views

Draw Vector Tangent to Point on Parameterized Curve [duplicate]

I define the vector function $\vec{r}(t)$ by r[t_] = {t, Cos[t], Sin[t]} The command r'[t] gives the vector tangent to the ...
2
votes
3answers
1k views

How do you show a cone inside of a sphere?

I have a sphere of radius 5 and a cone (i.e. z=√(x^2+y^2)) inside of it. I can show them separately, but I'd like to show them together. I've tried a few tricks with opacity, implicit specifications, ...
1
vote
0answers
285 views

Symbolic derivatives with vectors and matrices

I'm currently trying to solve some problems using symbolic vectors and matrices of arbitrary size. However, I have some problems with understanding and verifying the results: I defined the vectors as ...