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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.

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how can I construct binomial terms using the binomial function?

Basically, what I want to achieve is that for variable t and 1-t so the constructed terms are the Binomial(n,i),t^i *(1-t)^n-i, i goes from 0 to n, and I do not want to sum them, I want all the ...
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2answers
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Solving parametric equation

I am trying to solve these equations t + (a*Sin[t/b - h] + a)*Tan[θ] == x k + (a*Sin[t/b - h] + a) == y where a, b, h, and ...
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2answers
135 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 $x\in[-\pi,\pi]$. ...
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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'...
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1answer
27 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 ...
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1answer
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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. ...
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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 ...
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1answer
48 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} = -\...
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1answer
46 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: ...
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1answer
36 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
31 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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64 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
53 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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48 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 ...
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2answers
206 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 ...
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1answer
34 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
47 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
29 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 ...
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2answers
150 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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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 ...
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2answers
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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
33 views

FindInstance with a symbolic constant

Please consider FindInstance[m >= 0 && x >= 0 && x <= m, {x}] for which, I would like a parametric answer ...
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0answers
80 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 <...
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1answer
57 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 ...
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1answer
45 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 ...
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1answer
71 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 ...
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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 ...
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1answer
46 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: ...
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3answers
176 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. ...
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1answer
58 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
44 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
104 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 ...
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3answers
56 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?
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2answers
97 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
49 views
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1answer
60 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
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$$ (...
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How to find where a parametric curve overlaps itself, problem with calculation?

This should work? But it is giving me the wrong t values
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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
44 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
49 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 ...
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1answer
56 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: ...
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1answer
76 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 ...
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1answer
80 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 ...
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1answer
149 views

How to plot a rotated ellipse using `ParametricPlot`?

I'm plotting the von Mises yield surface using CountourPlot and ParametricPlot. With ...
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1answer
25 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
49 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. ...
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1answer
52 views

Changing ParametricPlot to ParametricPlot3D with NDSolve

I have some code that I am happy with: ...