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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Picking elements from separate lists and multiplying them

So I'm doing some instruction items about surface integrals. I've written the following code. it calculates curl and partial derivatives of the surface. I now want to create the following function, ...
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Help with code on integration

I'm trying to do a surface integral through a vector field of a disc. The problem says there is a vector field $\langle 0, y, -z\rangle$ and the disc is $x^2 + z^2 \le 1, y = 1$. The answer is $\pi$ ...
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Parametric Surface Integral Boundary Code?

I am having trouble using MMA to calculate 2 parametrized surface integrals. I'd be grateful for any fixes people can offer. I usually calculate surface integrals with the following code, which works, ...
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126 views

Parametric equations and eq. of tangent plane

I have written the following code to determine the equation of a plane tangent to a surface at a given point: ...
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Help on center of mass code

I have reviewed questions on MMMA Stack Exchange and found no help. Here's my problem and my code, which only partially works. I can't figure out my mistake. Help? Find the mass and COM of a wire in ...
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58 views

Exploring curl of a gradient of a scalar function

Suppose I want to explore $\nabla \times \nabla V$ where $V$ is some scalar function. It basically results in a zero. But I would only know why if I solve it on paper. I wanted to use Mathematica for ...
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How to plot integral of a gradient function

For $f : \mathbb{R} \longrightarrow \mathbb{R}$ continously differentiable and $\phi \in [0,\pi/2]$ let $$F(x) = \int \frac{f'(x)-\cot \phi}{1+ f'(x) \cot \phi} d x$$ be a clockwise 'rotation' of $f$. ...
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Issue with the Laplacian in Cylindrical Coordinates

I am using Mathematica 12.1.1 and am unable to get the correct result for a simple laplacian in 3D Cylindrical Coordinates. I want to reproduce the following result on Mathematica: But, I am only ...
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Can Mathematica evaluate vector gradients?

Can Mathematica compute vector gradients such as $$\nabla \lVert x \rVert ^2_2 = 2x$$ $$\nabla \lVert Ax - b \rVert = A^T (Ax - b)$$
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How to write a program on gradients and the path for steepest ascent?

I'm given two functions f[x ,y ]=Cos[x]*Cos[y]/(6+x^2+y^2) and df[x ,y ]=Grad[F[x,y],{x,y}] I was given a note that ...
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Understanding and visualizing Bessel function with complex argument

I have a vector field in polar coordinates $(r,\phi)$, which I wish to visualize and better understand. It represents the Electric field vectors for a given field distribution inside a circular ...
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Plotting list data of cross product of field vectors

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Triple Integral boundaries and solution

So I'm working on triple integrals, specifically on those where I have a region bounded by various surfaces. (In other words, the ranges for each integrals are not given, but must be calculated.) I ...
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Scalar potential function from 3D vectorial field

I am new at this forum and a beginner with Mathematica. Today I was studying multivariable calculus and I came with this problem. For example, in 2D case I have this code: ...
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A mistery in the documentation of the StreamDensityPlot command, and Is Abs' the same as Sign?

I was trying to decipher the documentation example ...
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35 views

JacobianMatrix Command Not Working Properly [duplicate]

This is what I get when using the command: ...
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1answer
93 views

Plotting a corrugated ribbon on a 3D Plot

I was assigned to write the following code: ...
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How can I make NDSolve aware of vectorial nature of an ODE?

I am trying to solve the equilibrium equation $\text{DIV } \mathbf P(\textbf{u}(x,y)) = \mathbf{f}$, where $\mathbf P$ is the stress tensor defined by $$ \mathbf P = \mathbf F + (1-\det\mathbf F)^...
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51 views

How to calculate the gradient in cylindrical coordinates in more efficient way?

I would like to obtain the gradient for the following function in cylindrical Coordinates ...
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111 views

Cannot derive `Norm` or `Normalize` when recreating Frenet Serret equations

I'm trying to calculate the torsion of a curve at a point using the following code: ...
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Eliminate doesn't work

I tried to define r by the polynomials a,b,c only. The result which I want is r=4/3 a. But this eliminate doesn't work! It is continue running without stop and without any output. Eliminate[{a == x[1] ...
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Why is ParametricPlot3D not producing a graph

I have the vector V = {2, y z^2, 3 y + z} I wanted to get a 3d parametric plot of V using: x[t] = Sin[t^2]; y[t] = t^2 - Cos[t]; z[t] = Sinh[t] - Cos[t]. So I did: <...
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Ket representation in mathematica

I have a simple case: I tried using ket representation for vectors in $\mathbb{C}^{2^2}$. I tired assing for Ket[] notatation from mathematica like this Ket[3] = $\{0,0,0,1\} $. We can assign it in a ...
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Functions of several variables composition

If we have two functions $G,F:\mathbb R^2\to\mathbb R^2$ then the mechanism $F\circ G(x,y)=F(G(x,y))$ gives us a new map $F\circ G:\mathbb R^2\to\mathbb R^2$ called its composition. In a "...
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How is Grad defined for array particularly in non-Cartesian coordinates?

This question can be viewed as a follow-up of What is the definition of Curl in Mathematica? First argument of Grad can be an array, but what definition does ...
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Find Solution to Exact ODE with 4 Variables?

OK, I give up. I was trying to use the solution in this post to solve an exact ODE with 4 independent variables. This works ...
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Aesthetic Constant Vectorial Field 3D-Plot

I am trying to 3D-Plot a constant Vectorial Field: ...
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1answer
45 views

Referencing the Component of a vector

If I were to define a vector r = {2, 0} + t*({5, 4} - {2, 0}) >>{2 + 3 t, 4 t} Sqrt[(D[r[1]])^2 + (D[r[2]])^2] How do I properly reference a single ...
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Line Integral with Vector Plot Parametric Plot and Show

How can I make different plottings of this line integral where $C$ is the square bounded by lines $x = \pm 1$ and $y = \pm 1$. $$ \begin{equation} \int_C 4y^3dx-2x^2dy \end{equation} $...
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How to reproduce `JacobianMatrix` function

I want to use the JacobianMatrix function in package VectorAnalysis, but I get the following warning message after running the ...
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32 views

Plot trajectory and angle of object using multivariable vector plot

I want to plot a projectile motion graph, with and without drag. So I want the x-axis to be the horizontal displacement. y-axis is the change in angle. z-axis is the vertical displacement. ...
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103 views

Help with simplification

Could anyone please help me simply the following expression ...
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2answers
52 views

About composition of functions (I don't want to use a vector variable function)

f2[x_, y_] := x^2 + y^3; g[t_] := {t^2, 3*t+1} $g$ returns a list, but $f_2$ is a two variable function. So, we cannot compose these functions: ...
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1answer
110 views

Efficiently finding spheres furthers apart along and perpendicular to a given direction

Setting I am dealing with a box of spheres, all having the same radius and inserted into a finite box size without any overlaps. Along a given direction $\mathbf v$, I am trying to find: (a) The two ...
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1answer
158 views

Generating random vectors using Mathematica and an inequality

Consider $n$-dimensional vectors $c^i = \left(c^i_1, c^i_2 ...c^i_n \right)$ , whose entries are complex and generated at random. These vectors are normalized such that $$|c^i|^2 = 1.$$ Using ...
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Obtain the vector potential and magnetic vector of infinite wire carrying charge

I'm working on the question above, but I'm really stuck for days. my goal is to implement the following Problem in Mathematica. Any help would be appreciated. I want to evaluate the following ...
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54 views

Find vectors describing two interconnected pyramids in Euclidean space

I need the help of competent linear algebra specialists in Mathematica. In the Euclidean space, two tetrahedrons are turned at different angles. Their vertices coincide with the beginning of the base ...
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1answer
59 views

Using Grad and NDSolve with vector variables

A simple orbital model might be developed like this: ...
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1answer
258 views

How can I use a unit vector notation found in physic texts?

In physics (I'm thinking of Taylor's Classical Mechanics or Griffith's Classical Electrodynamics) it is common to use "hat" vectors to denote unit vectors like $\hat{x}$ or $\hat{r}$. If I wanted to ...
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Error when trying to solve elastic PDEs using FEM: “Compile::argcompten: The comparison, LessEqual, is invalid for tensor arguments.”

I'm trying to solve the following linear elastic problem: The pairs of numbers beside each node is the coordinates in meters. The loads are in Newtons. The part of codes that probably have no ...
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2answers
182 views

Summations on Variables with subscripts

One of my equations uses a set of variables which ultimately for a set of certain values gives a list of 8 numbers: c=13.9506 (31 - k) following cc(sub k) = Round[Table[13.950621339931203...
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598 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 ...
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2answers
72 views

How can I concisely define a matrix-form partial derivative operator?

I have a vector $\boldsymbol{u}(x,y) = \begin{bmatrix} u_x(x,y) \\ u_y(x,y) \\ \end{bmatrix}.$ I would like to get $\boldsymbol{\sigma}(x,y) = \begin{bmatrix} \sigma_x \\ \sigma_y \\ \tau_{xy}...
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1answer
63 views

How can I take the divergence of a symbolic vector? [duplicate]

I would like to compute expressions that have the following form: $$\left(\partial_{p_1} - \partial_{p_2}\right)^2 \left(\partial_{p_1} - \partial_{p_2}\right)^2 \frac{(p_1-p_2)\cdot(p_3-p_4)}{p_1^...
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2answers
267 views

How do I get actual values from a Jacobian matrix?

I have a Jacobian function: D[{Sqrt[x^2 + y^2], ArcTan[x, y]}, {{x, y}}] It gives me a matrix with the formulas I need for my transposition matrix: ...
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52 views

How do you get a partial derivative of a vector to another vector?

I have a translation function between Cartesian and Polar coordinates: xi[xPrime_] := {xPrime[[1]]*Cos[xPrime[[2]]], xPrime[[1]]*Sin[xPrime[[2]]]} I now want to ...
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1answer
63 views

Computing the average curvature of a curve [closed]

Compute the average curvature of the curve $\qquad r(t) = ⟨t \cos t,\, t \sin t⟩\ \mathrm{for}\ 0 ≤ t ≤ 2π$. Use Mathematica to arrive at an exact value and its numerical approximation. Please include ...
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1answer
136 views

Visualising and detecting stacked oblate particles

Context: I am trying to learn how to visualize a box filled with oblate-shaped particles. These are in contrast to prolates which can be drawn using for example ...
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1answer
44 views

RecurrenceTable: numercial exception

When I added vector b into expression, it returned with RecurrenceTable::excptn: Value {2/3,-(1/3),2/3,-(1/3)} is a numerical exception. ...
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327 views

Solve the vector-matrix equation. Minimize the length of the desired n-dimensional vector

There is the following vector-matrix equation: $$\mathbf x^\top\mathbf M\mathbf x=\begin{bmatrix}x_1&x_2&x_3\end{bmatrix}\begin{bmatrix}a&b&c\\d&e&f\\g&h&i\end{bmatrix}...

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