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Questions tagged [parametric-functions]

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

2
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1answer
106 views

Calculating the sum of the lengths and plotting all curves on the same map

I have a curve like below; ParametricPlot[ FromPolarCoordinates[{Exp[(t + 0)*0.5], t}] // Evaluate, {t, 0, Pi - 0}, PlotRange -> All] This curve rotates ...
2
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2answers
82 views

How to evaluate the “Domain” of a Parametric Function?

In a simple example I try to calculate the time the solution x[t] passes a second time x[t]==1. ...
8
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2answers
192 views

Finding the point closest to a parameteric curve produced by a numerical method

Question How can I find the closest point to a parametric curve produced by a numerical method. General Context I have a parametric curve (which I will call $g$) produced from a averaging many ...
0
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1answer
45 views

Parametric and differential plotting [closed]

I was able to plot the differential equations, but can't figure out how to plot another set of parametric equations that are not differential equations. (i.e. {x[t], y[t]} = {vx0 t, 2 + vy0 t - 1/2 g ...
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0answers
43 views

how to go from 2 parametrized functions f(x) and g(x) to f(g) [closed]

I have two functions : f[x] g[x] and I would like to get : f[g] with an exact function or a numerical one. I thought to ...
5
votes
1answer
62 views

Model calibration with phase space data

Forgive me if this is answered elsewhere, I am new to Mathematica and this forum and have tried a number of search phrases to no avail. My question is very general but for example, suppose I throw a ...
0
votes
2answers
42 views

ParametricPlot table of complex functions in several graphs

Assume that I have a table of complex functions like Clear[p] Clear[M] M = 10; G = Table[Sin[i p] + p I, {i, M}] I want to ParametricPlot them in graphs, each ...
4
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1answer
44 views

Plotting a vector field embedded in a donut

I have the following code ...
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0answers
24 views

EDO with parameter, divergence and stop integration

I'm trying to solve an ODE which independent variable is time, where there is a parameter involved, let's say $\beta$. I need to plot the final solution in terms of $\beta$. The equations, initial ...
0
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1answer
95 views

numerical solution of nonlinear differential equation : parameter fitting

I want to fit data X-axis and Y-axis are L and P, respectively n'[L,t] == L a - b n[L,t]^2 - c n[t]^3, n[L,0]==0 a,b,c is independent parameters. P value is ...
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0answers
36 views

ParametricPlot with more than two parameters [closed]

This is a general question, and it actually was already asked before but for a case that was wisely solved (see here). I'm going to give a naive example to be clear: Let us suppose you have three ...
7
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5answers
239 views

Functional fixed points (ie fixed point of mapping from function space C[0,1] to itself)

I am looking for some tips or guidance as to what machinery in mathematica can help me get at this problem numerically. I am looking for fixed points of a mapping, but the objects in question are ...
3
votes
3answers
125 views

Plotting eigenvalue function along a path with correct coloring

This question has multiple parts to it. The setup is that I have a matrix that is a function of two parameters a and b. I wish to plot the eigenvalues of this matrix along a general path in the a-b ...
4
votes
3answers
111 views

Plotting an Equation Using ParametricNDSolve

I'm trying to plot the solution of a set of differential equations and see how the solution changes when the value of a certain variable de is changed. The equations have solutions to the values of de ...
0
votes
2answers
176 views

Plot on the surface of a Torus

I'm trying to plot a system with a variable (or field) $\theta(x,t)\in[-\pi,\pi]$ which is an angle at every position $x$. The positional argument $x$ itself is a periodic coordinate $x\in[-\pi,\pi]$. ...
3
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0answers
48 views

Plotting gradient and newton directions for parametric system of nonlinear ODEs

I have a bucket (system) of chemical kinetics models, a nonlinear dynamical system given by: where kf >= 0 and kr >= 0 are the parameters. The initial conditions are A(0) = B(0) = 1 and C(0) = 0. I'...
1
vote
1answer
35 views

How to draw a plane with ParametricPlot3D when f(x,y)==0?

I have the same issue (actually I have exactly the same prompt) as the creator of this topic: Draw two planes of Cartesian equation: y=3-x and z=2+x with Plot3D The answer I found there was really ...
0
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1answer
35 views

How can I optimize plotting the solution to ParametricNDSolve as a function of a range of values of the parameter?

I'm using ParametricNDSolve to find a solution to a set of first order ODEs which have one independent variable, z. The set of initial values contains a function of t. ...
0
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0answers
16 views

Polynomial interpolation using Wachspress construction to interpolate color on a quadrilaterial

My questions is how to use Rational Polynomial interpolants to paint the edges of a quadrilateral smoothly using 4 different colors. My tutor has taught this two-variable version of Pade expansion ...
1
vote
1answer
51 views

Taking the limit of a parametric function produced by ParametricNDSolveValue

I'm working on a project for hard-sphere scattering, and to solve the for the phase function $\overline{\delta}_l(k,r)$ I use the variable phase equation $$ \frac{d\overline{\delta}_l(r,k)}{dr} = -\...
3
votes
1answer
50 views

Drawing evenly spaced arrows and opaque sheet between curves?

I have a question about drawing arrows/sheets between curves. Suppose I have two 3-d parametric curves like shown below: ...
1
vote
1answer
41 views

Implicit and Parametric Plot

I am trying to graph the partials of two equations with respect to t, with both equations being implicit. I know I should be getting ellipses with the x-axis as the major axis. ...
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2answers
33 views

Shading between two regions of two separate parametric curves/function

I have two long functions g12 and g14 in terms of g2: ...
0
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1answer
78 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 ...
0
votes
1answer
59 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
50 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
230 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
votes
1answer
36 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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vote
1answer
48 views

Failure to plot a subset of curves using ParametricPlot

I wish to plot a parametric curve with parameters Γ,Δ,ϵ such that ...
0
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1answer
42 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
171 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
32 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
votes
2answers
43 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: ...
0
votes
1answer
36 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
84 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
102 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
49 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
72 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
60 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
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1answer
49 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
181 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
vote
1answer
64 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
50 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
3answers
111 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
63 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
107 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
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1answer
49 views
0
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1answer
71 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
48 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$$ (...