Questions about explicit functions expressed in terms of independent variables, i.e. parameters. Including approaches for rewriting functions using different parameterizations.

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0
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0answers
56 views

Can you help me reduce this? WolframAlpha's search bar has a character limit [on hold]

Trying to find the pursuit curve for the following illustration: First equation of motion: ...
2
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0answers
89 views

What is a good way to model fluid stream contours around airfoils?

I am an undergraduate student and am doing a project on conformal mapping for my complex analysis class. I have had one heck of a time trying to plot stream function contours to model fluid flow in ...
5
votes
1answer
71 views

Finding the correct boundary conditions to a specific problem

I want to reproduce the following problem in the figure: $$\phi''+c\phi'\sqrt{m^2\phi^2+\phi'^2}+m^2\phi=0$$ where $\phi=\phi(x)$ with $x \in (-\infty,\infty)$, $c=\sqrt{3/2} \ $ and $m=0.2$. ...
0
votes
1answer
64 views

ParametricPlot3D etc. with parameters satisfying an implicit relation

I need some help on plotting the curve generated by a vector, given its three components as a function of two parameters, e.g. s1 and s2, whose range are known, and they have to satisfy a given ...
-2
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1answer
46 views
1
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2answers
118 views

How to plot coupled Differential equations with changing parameters?

I'm a new user of mathematica. What I'm trying to do is following: I have two coupled non-linear differential equations. Say $x'(t)$ = $A− (B +1)x + x^2 y$ $y'(t) = Bx − x^2 y$ What I want is to ...
0
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1answer
44 views

Problem with combining Manipulate and ParametricPlot3D

I've beein trying to solve this problem but somehow I just can't combine Manipulate and ParametricPlot3D. ...
4
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2answers
196 views

How can I visualize a map $f:T^2\to T^2$?

Let $T^2\cong S^1\times S^1$ be the one-holed torus surface (say, embedded in $\mathbb{R}^3$) and say I have a simple-ish map $f:T^2\to T^2$ which I'd like to visualize. How might I do that? To make ...
0
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0answers
37 views

Problems solving differential equation with ParametricNDsolve for certain parameters

I'm working on a simulation of a physical problem for a few weeks now and I'm starting to get really frustrated about it. The problem itself is the stationary case of the heat diffusion equation in ...
0
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1answer
74 views

Transforming from implicit Cartesian form to a parametric form [closed]

First equation $((1.2 x)^2 + (1.4 y)^2 - 1)^3 - (1.3 x)^2 y^3 == 0$ I wanna transform it into a parametric equation. I spent a much of a day working on it without success. The equation describes the ...
3
votes
2answers
121 views

Computing powers of the operator using symbolic computation

Suppose $t\in\mathbb{R_+}$ - some parameter, $V: \mathbb{R}\to\mathbb{R}$ - some function. I have an operator $S:f\mapsto S[f]$ that maps a function $f$ to a function $S[f]$: $$ S[f](x) = ...
0
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2answers
123 views

How to define a formula-less function? [closed]

How can I tell Mathematica that $f(t)$ is a function of time without providing it with a formula? I want to write an auto Lagrangian calculator. And a derivative taker is needed which writes the ...
0
votes
1answer
62 views

NDSolve Surface Plot to Compare Initial Values

I am trying to solve a system of differential equations which model reaction kinetics using NDSolve. I would like to generate a surface-plot of the function value as a function of time and the initial ...
1
vote
1answer
82 views

Ugly rendering of curve with ParametricPlot3D and NDSolve [closed]

I frequently have this rendering problem when I plot a complicated curve with ParametricPlot3D, found by solving a differential equation with NDSolve : The curve should be more "regular" (it is ...
0
votes
1answer
50 views

Visualizing how a function varies as a parameter varies [closed]

I would like to plot the following function: \begin{equation} ...
4
votes
2answers
287 views

Is Mathematica capable of converting parametric equations into a function? If so, how?

I've been trying to find the formula for the offset/parallel to a sine wave. Not just the parametric equation, but the y = f(x) form. Here's what I've done so far: Read up on the parametric form and ...
3
votes
2answers
94 views

A parametrization for $\frac{\sin(x)}{x}$ as a revolution surface around $y$ axis

I'm looking for a parametrization for $\frac{\sin(x)}{x}$ as a revolution surface arround the $y$ axis. I have tried $X(x,y)=\Big(\frac{\sin(y)\sin(x)}{x},x,\frac{\cos(y)\sin(x)}{x}\Big)$. ...
7
votes
2answers
330 views

Plotting the image of a curve under a flow

I have some explicit time-independent vector field on the plane, and I would like to study how points evolve under the flow generated by this vector field. The flow is rather complicated and cannot be ...
1
vote
1answer
89 views

How do I plot a parametric family of curves given a list of parameter values?

I tried plotting the function shown below in Mathematica; however the plot showed nothing. Could you help me explain it? Note that here D' = 1- x. ...
4
votes
1answer
270 views

Solving the Frenet Serret equations for non-constant curvature and torsion, obtaining parametric equations

I wish to solve for the curvature and torsion functions $k_1 = \dfrac{1}{1+s^2}, k_2 = \dfrac{s}{1+s^2}$ using the Frenet Serret system and obtain the parametric equations for the curve. I need the ...
3
votes
4answers
226 views

ParametricPlot3D for only part of a sphere

I want to plot the region of a sphere that satisfies the equation $$ \tan\theta\geq-\frac{rz}{rx\cos\phi + ry\sin\phi} $$ where $rx$, $ry$, $rz$ are known constants. The spherical coordinates ...
2
votes
0answers
53 views

Plotting a parametric function that is highly nonlinear [closed]

Okay, so I'm having some trouble with some very badly behaved functions. I'll try to phrase the question in general terms to begin with, because the actual equations consist of about 12 numerical ...
2
votes
1answer
58 views

Plotting certain time points in a parametric equation? [closed]

I'm using Mathematica 5.0 and I have the following problem. I have the following parametric equation that I plotted successfully. ...
0
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1answer
82 views

ParametricPlot3D crashes Kernel when called repeatedly in loop

I have a parametric function surf[u,v]. It can be plotted successfully like this: ...
1
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3answers
121 views

Plot multiple functions with different but overlapping intervals

Suppose I numerically solve a differential equation by using sol = ParametricNDSolve[{y'[x] == b y[x], y[0] == 1}, y, {x, 0, 0.3}, {b}] And then I want to plot ...
0
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1answer
48 views

Simple grouping equations [closed]

I'm new in the Mathematica world. A very basic question. I have been using the command Eliminate on a set of equations as follow: ...
0
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1answer
56 views

Eliminate variable on multiple equations [closed]

I'm pretty new with Mathematica. I have to perform a really simple operation, but I'm really struggling with that. I have a set of 4 equations, for example (they can also be more complex): $ AA = 2 ...
3
votes
1answer
103 views

Plotting a finite series w.r.t. a parameter [closed]

So I would like to plot the series below: $$ S_q = k \frac{1-\sum_{i=1}^{W}(1/W)^q}{1-q} $$ where $k$ is a constant which I assume for now to be equal to 1 and $q \in \mathbb{R}$. However, for my ...
6
votes
1answer
85 views

Continuously varying tube radius

I'm currently trying to draw tubular neighborhoods of torus knots, which Mathematica's "Tube" function allows me to do quite easily. My question regards the appearance of the neighborhood: Is there ...
8
votes
1answer
272 views

How to add a fading trail effect in Animate?

I would like to add a smooth fading effect to the end of a curve, while it is animated. Here's a minimal working example which shows a particle moving on a circle (the circle is drawn while the ...
1
vote
1answer
83 views

Color of lines in ParametricPlot3D

I have a function of two variables which returns a vector of three components. For example func[l_,t_]:={ x=.... y=.... z=.... {x,y,z}} Now I ...
5
votes
4answers
143 views

How to correct the name of axis?

In the output of a code I can view that the same axe has two names "z" and "x". How could I correct this? The code is ...
3
votes
2answers
106 views

Plot a parametric function from $\mathbb{R}^2$ to $\mathbb{R}^2$

I want to plot the following function defined on $[-1,1]\times[-1,1]\setminus(0,0)$: $$ F(x,y,t)= \begin{cases} (1-t)(x,y)+t(1,\frac{y}{x})& \text{if}\ -x\leq y\leq x \\ ...
1
vote
1answer
93 views

PametricPlot3D vs ContourPlot3D

Basically, I don't know whether I am missing something mathematically fundamental or I misued Mathematica's functions. ...
3
votes
1answer
173 views

How to work with ParametricNDSolve?

Update 3: I got it. A small dumb mistake... It has to be Evaluate[xP[y]'[0] /. s10] like this. Oh well... Update 2: So if do this ...
0
votes
1answer
95 views

Fourier Series and epicycles - How to find the radii and angular velocities from a function's Fourier Series expansion

The following code is a bit clumsy, but it constructs a variable number (n) of epicycles using the values from the radii and angularVel tables that follows the path of a parametric given as a sum of ...
3
votes
2answers
92 views

Defining special function or variable for a derivative in mathematica

I have a question in Mathematica, I would appreciate it if you possibly answered me. What can I do for defining a special variable for derivative of arbitrary variable. For example, imagine I have a ...
7
votes
2answers
193 views

Parametric plot on multi-dimensional domain

I wish to plot all the points in 3 space that satisfy the following conditions. $$ (x,y,z) = (a^2+b^2, ac+bd, c^2+d^2) $$ for $a,b,c,d$ in some range. I have tried the following. ...
1
vote
0answers
67 views

Fitting data using ParametricNDSolveValue and NonlinearModelFit [closed]

I'm trying to evaluate the kinetics of the chemical reaction. For that I need to fit my experimental data to the kinetic equation. These are my steps in Mathematica. ...
5
votes
0answers
95 views

Find regions in which the roots of a third degree polynomial are real

I have to find the roots of a third degree polynomial in $\phi$ that depends from 3 parameters, namely $t,s,w\in \mathbb R$. In order to do that I've used the command ...
3
votes
3answers
120 views

Filling between multivalued curve and normal curve

I have a multivalued curve p1 (left curve) and a normal curve xpr2 (right), and I want to fill the middle region between them as blue, and the rightmost region as red. However, I get this extra ...
1
vote
2answers
82 views

Creating B-splines using a For Loop

I'm very new to Mathematica (as will make itself clear with this question) and I'm trying to create a program that makes b-splines to fit n points. I'm not quite sure how to reference the i-th point ...
1
vote
1answer
78 views

Solving PDE for a parametric function, using ParametricNDSolve

I've to solve a $4 \times 4$ matrix PDE which involves the following matrices: ...
3
votes
2answers
383 views

Solve stiff system by shooting method

I'm trying to solve a second order differential equation with the shooting method but, it appears to be a stiff system. This is worst for a larger parameter $\mu$. I've tried different methods: ...
1
vote
2answers
75 views

Need help getting the intercept of two lines in a ContourPlot

I am trying to find a set of parameters $\{\epsilon,\epsilon_b\}$, so that the two local minima have exactly the difference of 15.1 (see code below) and the left sided local minimum and the local ...
3
votes
0answers
88 views

Schwarz-Christoffel toolbox [closed]

Is there a toolbox for working with Schwarz-Christoffel transformations in Mathematica? More generally, is there a toolbox for visualizing conformal mappings in the complex plane? There are a lot of ...
2
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1answer
540 views

Plot a function for different parameters

Suppose I have a function that I want to plot for several values of a parameter all in the same window. For instance the function $f$ defined as ...
1
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1answer
81 views

Trajectories of system of parametric equations

I have to obtain plots of trajectories for (theta(t),u(t)) and then overlay them with a contour plot. The overlaying with the contour plot it is easy. What trubles me though is the trajectory part. ...
4
votes
1answer
103 views

Inverse of parametrized ellipse area

If you parametrize an ellipse (with the center, not a focus, at the origin) as: {a Cos[t], b Sin[t]} the area traced out from the focus (not origin) for a given ...