Mathematical vectors, operations on vectors and vectorized programming.

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1answer
324 views

How to fix errors in Gram-Schmidt process when using random vectors?

I first make a function to get a random vector on unit sphere in a swath around the equator. That is what the parameter $\gamma$ controls; if $\gamma = 1/2$, the vectors can be chosen anywhere on the ...
4
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1answer
155 views

How to use DSolve with vectors without decomposing into vector components?

Given a basic, two-dimensional ballistic trajectory problem, I can solve the equations of motion using DSolve (or NDSolve) by ...
4
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1answer
102 views

Superimposing ListLineIntegralConvolutionPlot with transparent noise over ListContourPlot

I have an array of 128x256 data points in a rectilinear array. For each point there is a 2D vector quantity and a scalar quantity (normalised to -1 <= x <= 1). I very much like the ...
3
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3answers
346 views

Multiply (not divide!) Vectors in a List by Their Own Norm

I wanted a set ("list") of 100 random vectors of dimension 2. I accomplished this already by generating a "list of lists" where the elements of the overall list are 2-dimensional lists consisting of 2 ...
3
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2answers
214 views

Orthogonal vector in two dimensions

Maybe this is really basic, but I couldn't figure it out. I would like to find the "hat vector" of a vector I defined: it's a vector orthogonal to the given one, assuming two dimensions. So for ...
3
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2answers
133 views

Color vector according to angle

One can use the function VectorColorFunction in VectorPlot3d to color vectors according to their norms. How to color vectors ...
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2answers
212 views

Simple Plot of Vector

I have a vector $<x(t),y(t),z(t)>$ constrained to a unit sphere. I am trying to plot what the vector looks like as time progresses. What would be the easiest approach to visualizing this? I ...
3
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3answers
533 views

How to pull scalars out of a function that should act on lists?

Suppose I have A = a vecA B = b vecB where a and b are supposed to be arbitrary scalars ...
3
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2answers
350 views

How to make Mathematica show matrices and vectors nicely

It shows me like {{0}, {1}, {0}, {-1}} . Is it possible to make it look like a vector, always?
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4answers
187 views

Pack Solve results into a vector

I am currently using a really easy function to get the eigenvectors of a corresponding eigenspace: ...
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2answers
1k views

creating vectors with normal distribution of lengths

First consider vectors of unit length, say on the unit sphere. Now I want to give some magnitude to these vectors and I want the magnitude to be chosen from the normal distribution. In one dimension ...
3
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2answers
155 views

ListPlot vector 3D circle line

I got a 2D vector with the following code. ...
3
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3answers
181 views

Plot a vector field over a line

This seemingly simple problem is giving me some trouble. I need to plot a vector field on a line, and for that I'm following what I found here. I try to create a mesh that contains two points and just ...
3
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2answers
100 views

Creating a tube with custom caps

I need a tube with only one end capped. I can do this relatively easily with: ...
3
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2answers
208 views

Vector Plot of a linearly varying cantilever

I want to drawing with Vector Plot a deflection and slope of a linearly varying cantilever. And with Contour Plot it works but with Vector Plot it didn't. Here is the code: ...
3
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1answer
284 views

Introduction to Vectors and NDSolve

I want to use NDSolve for a complicated equation that contains vectors. I am still new to Mathematica, and have really enjoyed what I have learned thus far. Concerning this question, I have already ...
3
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2answers
50 views

How to avoid 0 OverVector[F] to be evaluated as 0?

I am fairly new in Mathematica and I am trying to work with scalars and vectors. I decided to denote vectors using OverVector (as example, ...
3
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2answers
148 views

how can I make a control for my vector equation in my simulation?

I'm trying to build a control selector or menu for equations to put into my curvature simulations. However all the code I've tried hasn't worked.Does anyone know how I could make a control selector or ...
3
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2answers
602 views

Ploting a 3D vector field using Manipulate, VectorPlot3D and NDSolve

My aim is to plot a vector field of the following system with a few trajectories: $$r'(t)=i-l.r(t)-\text{ux}. r(t). x(t)-\text{uy}. r(t). y(t) \\ x'(t)=\text{ex}. \text{ux}. r(t). x(t)-\text{mx}. ...
3
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2answers
126 views

How to extract state vector after NDSolve for subsequent re-use?

I'm using code like this: ...
3
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1answer
136 views

How to remove recursion, and write it functional and efficient way?

I wish to implement the following recursion efficiently. ...
3
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1answer
937 views

Normal and Tangent of Acceleration in 3D

I am trying to find the normal and tangent of acceleration. I know the formula for the tangent of acceleration is $((Acceleration . Velocity)/(Velocity.Velocity))*Velocity$ and the normal of ...
3
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1answer
229 views

How can I independently move vector components (in 2D)?

Here's what may well be a simple problem that I have been having difficulty with: There are two connected vectors, v1 and v2, such that: v1 begins at the origin and and ends at point a1 v2 begins ...
3
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1answer
76 views

Finding the attractors of the vector field constructed as the gradient of an interpolated 3D scalar field

I have a list of data existing as {{{x, y, z}, f},...} from which I construct a 3D interpolation function using Interpolation[ ]. I am able to construct a vector field from the gradient of this scalar ...
3
votes
1answer
451 views

How to control the length of vectors in VectorPlot

I want a slope field for a scalar differential equation. For simplicity I have chosen $dx/dt=rx$, where $r$ is a parameter. I used VectorPlot for the slope field as you can see from the code below. ...
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499 views

Extract common factor from vector or matrix

I can't believe this hasn't been asked before but I can't find anything. Is there a way to convince Simplify or FullSimplify to ...
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4answers
117 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: ...
2
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3answers
963 views

Adding a Sphere onto an existing 3D plot

I have a 3D plot. I need to add a small sphere marking the starting point, r[t] == 0. I'm pretty new at Mathematica and would greatly appreciate some help. ...
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2answers
1k views

Using the epsilon tensor in Mathematica

I'm having a great deal of trouble getting started on a weekly homework assignment in Mathematica. The assignment requires we use the epsilon tensor which is apparently built into Mathematica as ...
2
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1answer
149 views

Derivatives of vectors

I have an issue with derivatives of vectors ...
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2answers
174 views

How to initialize several elements per iteration with Table?

I would like to initialize this kind of vector : {0,0,1,1,0,1,0,1,1,1,1,1} with Table. I tried ...
2
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1answer
211 views

Orthogonalize method, keeping to binary vectors

The built in function: Orthogonalize[m] where m is a list of vectors returns a orthogonal basis for m. However, I want to stick to the binary field. However, I ...
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2answers
208 views

How can I express this recurrence function in Mathematica?

\begin{equation} r_{i+1}=r_{i}+V_{i}{\Delta}t \end{equation} Where \begin{equation} V_{i}=(0.01, 0.40) \end{equation} and ${\Delta}t$ is the difference in time. My implementation (this is for ...
2
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1answer
826 views

Plotting 3D Vector Field in one plane

I want to plot a vector field F={Fx, Fy, Fz}. However, I only want to plot it in one plane (say, z=0). When I use ...
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2answers
1k views

Circular Orbit Velocity in Vector Components

I'm trying to find out how to calculate the initial velocity needed to keep a spacecraft in a circular orbit around the Earth given its initial position and an initial angle theta in a Cartesian ...
2
votes
1answer
672 views

Making a ListVectorPlot3D from data in an external file

I have a .dat file with six columns: {x y z vx vy vz}, where x, y, z are space coordinates and vx, vy, vz are the vector components. How can I use this file to get ...
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3answers
2k views

Phase space vector field [duplicate]

I have a system of non linear equations and from NDSolve I get the solution. I plot the phase space with ...
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3answers
87 views

Making a list of functions

Suppose I have the following equation system to solve: x(t_):={x1(t),x2(t)}; DSolve[x'(t)==x(t),x(t),t] This code works fine, but now suppose that instead of 2 ...
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3answers
75 views

Referring to the components of a vector within a sum

I feel like I'm missing something obvious here, but.... I'm playing around, trying to do the standard deviation for my stats homework (don't worry, I already worked out the answer by hand), and I ...
2
votes
1answer
62 views

Plotting Vectors in Mathematic at lat/long positions

I have some current data that I want to plot in Mathematica. The first two columns are the latitude and longitude respectively (longitudes are negative b/c it is west of the prime meridian and all ...
2
votes
1answer
113 views

How can I use parts of lists with Dynamic?

I'm a newbie - what am I doing wrong? I want to use parts of lists (vectors) in calculations but Mathematica will not evaluate anything that involves parts of lists that update dynamically. Is there a ...
2
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3answers
143 views

`Solve` with variables as single vector

Say I have a set of equations where the unknown variables are the elements of a vector $c=(c_1,c_2,\ldots)$ and want to solve it for $c$. Is there a way to do this with ...
2
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1answer
467 views

Solving vector equations

I made this very simple module to try and solve vector X: ...
2
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2answers
138 views

How can I visualize an array of very small vectors spaced on very large grid? [duplicate]

I have data in the form points = {{1, 1, 1}, {1, 1, 2}, ...} vectors = {{2, 2, 5}, {2, 1, 7}, ...} Can somebody help to edit this data so I can ListVectorPlot a ...
2
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1answer
136 views

Operator operation

There are two basic operators r={x,y,z} and p=-I*h*{D[#,x] , D[#,y], D[#,z]} &. The angular momentum operator is defined as ...
2
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1answer
35 views

N-Dimensional vector from scalar

Is there a way in Mathematica to create an n-dimensional vector, where each element is a given scalar? I have tried the Array function, as the documentation center ...
2
votes
2answers
158 views

Returning the 3-dimensional vector from a skew symmetric matrix

I'm trying to write a function that takes in a skew symmetric matrix and returns the corresponding vector. When I write the following code, it works when I leave it as variables, but it does not work ...
2
votes
1answer
219 views

Taylor expansion of function of vectors—simplifying the output

I've got a real-valued function of several vectors $f(u,v,w)$ formed by taking scalar products of linear combinations of the vectors, I want to Taylor expand around small $v$ by writing $$f(u,\delta ...
2
votes
1answer
415 views

Plot Piecewise-Smooth Vector Field.

I want to plot a piecewise-smooth vector field. For instance: $F_1(x,y) = (x^2 + y^2, y^2)$, $F_2 (x,y) = (2xy,2xy-x^2)$ and $H(x,y) = x-y$ $F(x,y) = \begin{cases} F_1(x,y) \text{ if } H(x,y) ...
2
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2answers
765 views

How to expand a general expression in cross and dot product in Mathematica

I am looking for a way to simply the general expression in cross product and dot product with general vectors. I got a help in How do I simplify a vector expression? but soon I find that it doesn't ...