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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.

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0answers
5 views

ParametricPlot two Piecewise functions

I am trying to ParametricPlot two Piecewise functions. Here are my two Piecewise functions: ...
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2answers
14 views

Shading between two regions of two separate parametric curves/function

I have two long functions g12 and g14 in terms of g2: ...
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0answers
41 views

Visualize embedded and immersed Klein bottle

Answers at How to visualize a 4-dimensional parametric surface? give functions for producing images of 3D projections of 4D embeddings of the Klein bottle. Is there a way to get such a 3D projection ...
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1answer
50 views

Estimating parameters for pair of differential equations efficiently

I'm trying to estimate the parameters for the following pair of differential equations ...
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0answers
45 views

Parametric solution of a system of two nonlinear ODEs with data describing only one the functions

I have the following pair of nonlinear ordinary differential equations ...
3
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2answers
186 views

Solving a non-linear ODE system with ParametricNDSolveValue

I'm trying to solve a non linear ODE numerically with ParametricNDSolve, but as far as I got is shown below. My problem is to set the find root correctly. What I ...
2
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1answer
31 views

Working Precision warnings for ParametricPlot

I wish to plot a series of parametric curves for the following function called poly that has five parameters (Γ, ...
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1answer
45 views

Failure to plot a subset of curves using ParametricPlot

I wish to plot a parametric curve with parameters Γ,Δ,ϵ such that ...
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1answer
22 views

How to combine a ContourPlot with a Manipulate[Parametric Plot]

I have this code of an orbit at a Lagrange Point of the Sun-Jupiter system ...
6
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2answers
121 views

How to visualize a 4-dimensional parametric surface?

What are some good ways, using ParametricPlot3D or otherwise, to visualize a surface (taking 2 real parameters) embedded in a 4-dimensional space? Specifically, ...
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0answers
26 views

How to find ranges of values where specific conditions are true?

I'm trying to get Mathematica to solve a particular inequality in terms of the variables (and constants) of interest to find where the inequality holds as true. Specifically, I have three functions of ...
3
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2answers
36 views

Nesting ParametricNDSolveValue

I have a problem nesting the function ParametricNDSolveValue. The documentation does not help so I hope to find some answers here. A minimalistic example for my problem is: ...
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1answer
31 views

FindInstance with a symbolic constant

Please consider FindInstance[m >= 0 && x >= 0 && x <= m, {x}] for which, I would like a parametric answer ...
3
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0answers
73 views

The actual polynomial behind a BezierFunction

Let's say I have the following Mathematica code pts = {{0, 0}, {1, 1}, {2, -1}, {3, 0}}; F = BezierFunction[pts] How can I find the actual polynomial of the <...
3
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1answer
43 views

Plot Legends in 3D Parametric Plot with Color Function [duplicate]

I have two parametric space curves with different line styles plotted with ParametricPlot3D, with a ColorFunction applied. How ...
2
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1answer
42 views

ParametricNDSolveValue with coupled DEs and manipulation

How do I separate the solutions to these coupled DEs in the plot? I want to plot the solutions to these equations at time t=7 as a function of parameter ...
1
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1answer
69 views

Abstract vector algebra with scalars

I am interested in expanding a vector expression in terms of the scalar parameter, but it doesn't give the expected result ...
1
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3answers
53 views

How can I limit the plot of $f(x,y)=\rm{cons}t$ to the contour that passes through an specific point?

I want to plot a curve given by $$f(x,y)\equiv y-y^3+3yx^2=0,$$ that passes through $(0,0)$ and $f(x,y) \to + \infty$ as $|x|,|y| \to \infty$. I thought of using ContourPlot to do so but when I use ...
3
votes
1answer
44 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: ...
8
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3answers
165 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 the picture in Wikipedia: using equations such as those outlined here. ...
1
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1answer
51 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 ...
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0answers
38 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 ...
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3answers
98 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
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3answers
41 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
90 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: ...
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1answer
47 views
0
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1answer
50 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 ...
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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$$ (...
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5answers
423 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
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1answer
75 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\...
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1answer
43 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 ...
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1answer
42 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
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1answer
49 views

NDSolveValue in NDSolveValue

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

Save WhenEvent result in a table

I have a set of coupled differential equations of functions which evolve (increase) monotonically: ...
1
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1answer
65 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
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1answer
58 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
122 views

How to plot a rotated ellipse using `ParametricPlot`?

I'm plotting the von Mises yield surface using CountourPlot and ParametricPlot. With ...
1
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1answer
24 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: ...
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1answer
39 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
42 views

Changing ParametricPlot to ParametricPlot3D with NDSolve

I have some code that I am happy with: ...
3
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1answer
115 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
137 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
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1answer
44 views

Restricting domain in ParametricPlot

How would one restrict the domain on a ParametricPlot? For example, I have the following plot: ...
4
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3answers
140 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
49 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
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1answer
73 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
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1answer
54 views

Problem with ParametricPlot 4

Writing: ...
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2answers
187 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
60 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: ...