# 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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### 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 ...
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### Singularity or stiff system in ParametricNDSolve

I have following parameters and equations(it's a complex one, please check it :) ): ...
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### 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. ...
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### 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 ...
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### 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. ...
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### How can I substitute values into this set of equations?

I'm new to Mathematica and I'm trying to solve this set of trig equations (I'm not exactly sure if the syntax looks correct): ...
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### 3D Arrow path along a surface

I have the following two surfaces, created by the following functions ...
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### Marking with Mesh, Distinct coloring, Ticksing, and Plotting table of complex function with parametric plot

Here is my todo list and what i've done: Using FrameTicks on specific points only (failed). Plotting six graphs with Table on <...
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### Solving multiple differential equations parametrically

I have the following code, where I am trying to solve one set of differential equations parametrically. I then want to use this solution to solve another equation parametrically. However, I get the ...
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### How to get the intersection between circle and rectangle?

Consider two figures: a rectangle with coordinates $(x_{min},y_{min}), (x_{min}+dx,y_{min}+dy)$, and a circle. The latter has a radius $R$ and is located at the center of the coordinate frame. How to ...