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

3
votes
1answer
35 views

Parametric Plot - Opacity Changing Along Line

How would one have the trajectory in a parametric plot go from a higher to lower opacity? Suppose the following code for example: ...
4
votes
2answers
113 views

Issue Plotting Torus Link

I'm having an issue plotting torus links in Mathematica. What I'm trying to generate is a (2,8) torus link like the one in picture here:https://en.wikipedia.org/wiki/Linking_number Using equations ...
1
vote
1answer
43 views

Solving an ODE System with Multiple Initial Conditions

I am trying to use ParametricNDSolveValue to run ODE simulations with multiple initial conditions then plot the results with ...
0
votes
0answers
34 views

RegionFunction parametric or piecewise definition

Hi I want to plot a contourplot of a given surface over an specific region only. I have used the RegionFunction option for it. Now the problem is that the regions I need to plot are defined by ...
0
votes
0answers
101 views

Approximate the relationship between 6 nonlinear functions involving elliptic integrals

I am trying to solve a physics-related problem, which results in approximating a relationship between 6 symbolic functions $F_1(\alpha,\beta ,x_0,y_0),F_2(\alpha,\beta ,x_0,y_0),...,F_6(\alpha,\beta ,...
0
votes
3answers
96 views

Circle to Square Homotopy Generalization

I was looking for a nice visualization of the homotopy of the square to the circle. I produced the following code. Albeit, it isn't great, but it works out OK. My question is: Is there a better ...
1
vote
3answers
34 views

How to extract maximum value coordinates from ParametricPlot of function

I have a ParametricPlot ParametricPlot[{Sin[x], 2 Cos[x]}, {x, 0, 2 π}] How to know the maximum value on Y-axix and X-axis?
3
votes
2answers
85 views

Solve for constants of time-varying function that make the function derivative equal to zero

I have a system of ODE's and I want to check if a function of the variables is a conserved quantity of the system. My system of ODE's is similar to this one: ...
0
votes
1answer
46 views
0
votes
1answer
47 views

Plotting solution of ParametricNDSolve not possible for needed parameter range

I wish to numerically solve a parametric decay model. The system of equations is fairly simple. But plotting the solution for a wider parameter range is not possible (see code). Mathematica throws 2 ...
0
votes
1answer
47 views

Solving a completely variable equation

Suppose $f$ is an undetermined function which we want to obtain its form. We just know that it is coefficients of the below expansion as follows enter code here$$ (...
6
votes
5answers
416 views

How to find where a parametric curve overlaps itself, problem with calculation?

This should work? But it is giving me the wrong t values
1
vote
1answer
74 views

This complicated integral using numerical integration

I want to do the following integral $$ \int\limits_{-\pi/2}^{\pi/2}\dfrac{(k_{up}\cos\phi)\cdot(k_{down}\cos\alpha)}{k_{up}\cos\phi+k_{down}\cos\alpha}\cos{[(k_{up}\cos\phi-k_{down}\cos\alpha)x]}d\...
0
votes
1answer
41 views

How to plot some but not all of the solutions generated by ParametricNDSolve

My question is about the syntax of plotting solutions of ParametricNDSolve but not all. Specifically how can I plot just $x_1,x_2,x_3$ not $x_1,x_2,x_3,i$. My ...
0
votes
1answer
34 views

Can't get parametric NDSolve to work for three ODE system

Below is code to simulate a three ODE system. When running the code I get no errors put no output is empty as well. Because of the lack of errors I needed Code ...
0
votes
1answer
41 views

NDSolveValue in NDSolveValue

I would like to implement a sort of Euler explicit manually. I have this code ...
0
votes
0answers
38 views

Save WhenEvent result in a table

I have a set of coupled differential equations of functions which evolve (increase) monotonically: ...
1
vote
1answer
52 views

ParametricNDSolve with variable initial conditions [duplicate]

I have a large set of coupled non-linear first order ODEs describing the time evolution of multiple variables a[t]....z[t]. For most of these, I have fixed initial ...
1
vote
1answer
52 views

How to find the parametric equation of the von Mises yield function?

The von Mises yield function is given by: $ \Phi(\sigma_1,\sigma_2)=\sqrt{\sigma_{1}^{2} +\sigma_{2}^{2}-\sigma_{1} \sigma_{2}} - \sigma_y $ were $\sigma_1$ and $\sigma_2$ are the principal ...
2
votes
1answer
97 views

How to plot a rotated ellipse using `ParametricPlot`?

I'm plotting the von Mises yield surface using CountourPlot and ParametricPlot. With ...
1
vote
1answer
23 views

Graph of a parametric curve that depends on an integral

I want to plot the following function: I have tried to define the function with this code: ...
1
vote
1answer
36 views

ParametricPlot3D coloring based on whether function located inside/outside of another parametric function

I have two parametric shapes: an inclined ring and an elliptic cone whose vertex lies along the x axis. ...
2
votes
1answer
37 views

Changing ParametricPlot to ParametricPlot3D with NDSolve

I have some code that I am happy with: ...
3
votes
1answer
111 views

Plot the curve of a group of parametric equations [closed]

This question is about how to use MMA to plot a curve from solution of a group of parametric equations. To take an algebraic equations as an example, like: \begin{align} x^2 - y^2 &= t^2 \\ xy &...
4
votes
2answers
121 views

How to do a DensityPlot on a ParametricPlot

I have some code that works nicely, for what I want, but when I try to get a DensityPlot or ContourPlot, it will not work as it ...
0
votes
1answer
43 views

Restricting domain in ParametricPlot

How would one restrict the domain on a ParametricPlot? For example, I have the following plot: ...
4
votes
3answers
137 views

Level sets of a parametric plot (3D)

I am having difficulty getting the level sets of a 3D parametric plot. I have a parametrized 3D surface that I suspect is self-intersecting and one way to see this visually is by plotting the level ...
1
vote
1answer
43 views

2D 'fill' for 3D helix

I have made a simple helix using ParametricPlot3D: ParametricPlot3D[{Cos[x], Cos[x], x}, {x, 0, 10}] I want to add a a continuous 'fill' connecting the curve to ...
0
votes
1answer
66 views

Plotting Two Components of NDSolve using Parametric Plot

Right now, I'm using this set-up to calculate one part of my differential equation function. ...
0
votes
1answer
51 views

Problem with ParametricPlot 4

Writing: ...
-1
votes
2answers
175 views

System of $n$ nonlinear differential equations [closed]

I'm trying to model the following system of $n$ nonlinear differential equations: $$ \dot{P}_i(t) = \sum_{1 \, \leq \, j \, < \, i} R(p_{ji}) - A(p_{ji}) + \sum_{i \, < \, j \, \leq \, N} A(p_{...
0
votes
0answers
56 views

Nonlinear time delay system: phase portrait plotting

I'm trying to plot a phase portrait for the nonlinear model with delays (I know that the phase portrait is an infinite dimension, but I want to treat the delay as a parameter). My system: ...
2
votes
1answer
54 views

How to create such 3D curve embeded in a certain hyperboloid

The following hyperboloid surface is created by: ...
0
votes
1answer
42 views

Using ParametricNDSolve solution in FindRoot with a complex valued unknown

I want to find the parameter N by solving the FindRoot, ...
0
votes
0answers
38 views

How to make the plot as a function?

I am trying to plot a graph, and assign a name p1 to it. The curves would have a different pattern when the parameters v changed,...
0
votes
0answers
65 views

ParametricPlot - Several curves by different parameters

I am trying to plot a set of curves f(a,b,t) along t with a,b = -10, -9, ..., 9, 10. I can use Manipulate to draw 1 curve, and then change the curve shape by ...
3
votes
1answer
51 views

Unexpected behavior of `Exclusions` in `ParametricPlot`

I'm using Mathematica to prepare some teaching materials based on the discussion of the damped, driven pendulum in Chapter 12 of Taylor's Classical Mechanics. This involves using ...
0
votes
1answer
40 views

Looping on ranges (Modular iterations)

Is it possible to make the following code modular, so that it works up till depth n, and returns an array of all possible combinations for used{}? ...
1
vote
1answer
81 views

The right plot to use for bifurcation diagram

I have on my hand the differential equation $ \dot{u} = ru(1-\frac{u}{q})-\frac{u^2}{1+u^2} $ for which I need to analyse its bifurcations. I know that the bifurcations occurs at $ q(u) = \frac{2u^3}{...
0
votes
0answers
70 views

Modelling the parameters of a function in Mathematica

This question is related to the question asked on Cross Validated SE: Link to the question. I am trying to model my data, which is the response to a ray of light on a film screen, using the ...
0
votes
0answers
43 views

How is the scale of ParametricPlot3D determined?

I define a couple ParametricPlot3D planes like so; ...
2
votes
1answer
93 views

Plot several parametric curves

I'm trying to plot two parametric graphs as follows: ...
0
votes
0answers
23 views

Custom Function Return Value Error

I have created the following function which calculates the equation of a curve given it's slope as a derivative and a point. ...
1
vote
2answers
132 views

Fitting data to the model issue

I am trying to to fit the data set to an SEIR model, however, I have encountered several problems while doing so and can not make it function.. Here is the most basic version of the code as well as ...
1
vote
1answer
112 views
1
vote
1answer
77 views

ParametricPlot shows nothing for NDSolve solutions

I want to plot x'[t] as a function of x[t] (phase space) with PararametricPlot but mathematica shows nothing i dont understand what the problem is.this is my code: ...
1
vote
2answers
57 views

Parametric plot for Pressure-Volume Curve

I am attempting to plot a PV curve using two functions that rely of time, one for pressure and one for volume. When I run my code I only get a straight line along one axis. I am doing something ...
2
votes
2answers
140 views

What is the most effective method of making function which should be different for real and integer arguments?

Which of the following 2 methods is better for heavy serial calculations? Method 1: f[x_Integer]:=Module[{...}, ...] f[x_Real]:=Module[{...}, ...] Method 2: <...
0
votes
0answers
30 views

Why does this minimization with parameters does not work?

This statement: Simplify[Minimize[{Exp[3 q], q >= 0}, q]] Returns correctly: {1, {q -> 0}} But this statement: <...