# 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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### ParametricNDsolve with initial condition dependent on parameter?

I want to use ParametricNDSolveValue' to solve pdes with initial conditions dependent on the parameter. To simply the question, I modified the mma example as following. The intial one is ...
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### I need formula of function that decrease no linearly from x to y [migrated]

I need a formula of function that decreases no linearly from x to y over a set of iteration for example -1+t*((-1)/Max), this formula decreases linearly from 2 to 0 where t=0,1,2,..., Max. can I make ...
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### Table of surface Parametric draw

I'm trying to reproduce this kind of graph for a spherical cap, with different span ratios. I tried with this: ...
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### How to solve \[Theta]23 from the following equation?

How do I solve [Theta]23 from the following equation? ...
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### Parametric Optimization In Mathematica

I want to solve the following problem: $$\max_q \dfrac{q}{a}\left[ (-\log(1-q))^{-a} - (-\log(q))^{-a} \right]$$ subject to $1\geq q \geq 0$ for each $a\neq 0$. Here is the code I used: ...
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### use of parametric ndsolve with a constraint

I want to solve differential equation $$\frac{y''[x]}{(1+y'[x]y'[x])^{3/2}} = -a -y[x]/ \sqrt{2} + x/ \sqrt{2}$$ subject to boundary condition $y(-1) = y(1) = 0$ for some value of $a$. $a$ is found ...
44 views

### Defining parametric function resulting from DSolve

I am trying to define a function that is a solution of a simple ODE with a parameter, for example ...
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### How to get a specific component of an equation without hardcoding? [closed]

Say I define an equation line[t_] = {t, 2t, 3t}. What code will define x[t] = t, y[t] = 2t, ...
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### How to make Sphere Transparent using ParametricPlot3D

This is the code I used Edit: This is the full code to create this image ...
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### How to table ParametricPlot with parametric value

I can plot this code ...
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Writing: ...
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### Unpacking a Mathematica expression returned by DSolve

I was trying to solve a system of differential equations in Mathematica and had troubles understanding what the solution looked like. So I wanted help to unpack it. I had a system of two coupled ...
78 views

### Singularity or stiff system in ParametricNDSolve

I have following parameters and equations(it's a complex one, please check it :) ): ...
79 views

### Does mathematica cache the interpolating function from ParametricNDSolve?

I want to evaluate the solution of a system of non-linear ODEs using ParametricNDSolve. The output of ParametricNDSolve is a ParametricFunction object. Let's call it $f_\theta(t)$, where $\theta$ is a ...
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### ParametricPlot3D with variable plot limits

I would like to use ParametricPlot3D in the following general way: ParametricPlot3D[\[Sigma][u,v],{u,0,2Pi},{v,-f[u],f[u]}]. ...
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### How can I combine two parametric plots in a continuous one?

I'm studying the Ekman spiral for piecewise uniform viscosity. So I have two velocity components (u,v) for every layer. One pair for the sufrace and one pair for the layer below. ...
78 views

### Error when integrating with constants?

I'm trying to integrate an ellipse: (x^2)/alpha^2) + ((y^2)/beta^2) = 1. I am not sure if I should have insert constants for alpha and beta or if there's a way to keep them there. This is my code <...
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### How to find absolute minimum with NMinimize

So I have a trefoil and twisted cubic that are very close to intersecting but do not. I know NMinimize can be used to best approximate the minimum, but it ...
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### Plotting a parametric function on xy, xz, and yz planes

I'm trying to plot a trefoil with a parametric function in Mathematica. How would I do that? I know I can use Parametric3D to depict all of it but how do I project it on the XY, XZ, and YZ planes? It'...
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### Plotting equation of motion in mathematica [closed]

Suppose I have an equation of a moving body in Newtonian Mechanics e.g. $ax^2=(b/t^4)+(c/t^2)$ how can I plot a x-t graph in mathematica with a range for the constants a, b and c from 0 to 5 with ...
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### Animating a Parametric Plot of Planetary Motion

I have been trying to make a simple animation of planetary motion, but I can't seem to get it to work. I'm still new to this program so I am not sure how to make it work. Can anyone help? Here is my ...
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### How to initiate a matrix with indexed parameters [closed]

I couldn't find it in the documentation, so I'm posting it here. I want to create two by two matrices as follows:  W = \begin{bmatrix}w_{11} & w_{12} \\ w_{21} & w_{22} \end{bmatrix}, V = \...
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### Spheroidal Harmonics

There is a (scalar) field P varying on a spheroid (squashed) surface. This field is a function of four independent components ...
88 views

### How to Create Lissajous Figures for Driven Damped Pendulum (as an animation/with Manipulate)

I wanted to know how can I generate a Lissajous plot for the forced driven pendulums (but for one pendulum in my case): (https://demonstrations.wolfram.com/ForcedPendulumsWithDamping/). I tried using ...
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### Converting a Non-Simple Closed Curve in an Image to a Parametric Equation

I would like to generate a parametric equation for a non-simple closed curve defined in a 2D image (shown below). This is the same problem as described in this question for simple curves. However, ...
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### Avoiding/skipping singularity error in ParametricNDSolve

I've looked up a few examples of similar errors for ODE's with singular points, but have yet to figure out a way to solve this problem for my case. A simple patch up where the singular point is '...
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### How to solve integro-differential with parameters iteratively?

I am trying to solve an integro-differential equation and tried using one of the answers that I found in a related question: Numerically solve an integro-differential equation The difference is I have ...
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### Plotting multiple dependent variables with DSolve (projectile motion with air resistance)

I wrote a working code that plots what I need using DSolve and parametric plot. Here's an example of what it plots (and code is at the bottom). However, I want to be able to plot multiple graphs on ...
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### How to solve this set of PDE equations? I tried ParametricNDSolve, but

I am tring to solve set of PDE equations with parameters of v[z],q[z],T[z,t,r]. Below is my ...
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### Issue with ParametricNDSolve and Table

I have a differential equation, I plot it for different initial values by using ParametricNDSOlve. Code - ...
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### NSolve with ParametricFunction

I have solved a SDE with ParametricNDSolve: s = ParametricNDSolve[ {p1, m1, p0, m0}, {P, m}, {r, 0, 1}, {m, k, e, Cnew} ] And now I want to treat the ...
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### Plot with three functions and three parameters [closed]

I think my code doesn't have any problem but the program shows me this error and I'm confused! Plot::argr: Plot called with 1 argument; 2 arguments are expected. ...