# 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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299 views

### Replace elements of a list based on a function

I have a function of k (written in the form of a table/list to get values) for 16 integer values from 1 to 16: f = Table[3*k*k, {k, 1, 256}] I want to replace ...
26 views

### How can I use Parallel Computing to speed up ParallelSum process with symbolic functions?

How can I speed up the code below using Parallel Computing? I have M.12.0.0 on a workstation with these specifications: Architecture: Ubuntu x86_64 RAM: ...
69 views

### How can I make a projection of ParametricPlot3D onto 2D surface without shading?

I have a Parametric Plot that has very high and low values. I used this answer Project RegionPlot3D to 2D using hue/color function to show third dimension to project the surface onto the 2D plane. ...
46 views

### How can I plot Trajectory of 3d parametric plot?

x1 and y1 are constants. I have plotted ParametricPlot3D. ...
52 views

### ParametricNDSolve for a system of 4 non-linear ODEs and plotting the solutions

I have four coupled first-order non-linear differential equations, denoted as: A1[x], A2[x], ...
128 views

### Problem with FindFormula for experimental dataset [closed]

I have a dataset whose mathematical model is unknown. There is my code. ...
82 views

### Combine different kinds of plots [duplicate]

how can i combine thats plots: ...
30 views

### Parametric field Plot

i want to plot this field: G(x,y,z) = (0,0,-b^3(x^2+y^2)cos(b^2(x^2+y^2))) with the parameter b>0. Is it possible to do that? if yes,how can i do that?
114 views

### Simplify Vs FullSimplify

I performed an integral and received an extremely long answer. I tried running FullSimplify on the answer, and after 72 hours gave up. Does ...
268 views

I have a list of coordinates that make a near-parabolic graph, which I managed to fit and calculate the curvature. However, the curvature only outputs a equation. Is there any way to calculate the ...
40 views

### Find Arc Curvature From List of Coordinates and NonLinearModelFit

I have coordinates as a list, and I can fit it almost perfectly with an equation. I'm just curious as to how I can find the curvature of this arc. I've tried using ArcCurvature, but I'm not sure how ...
29 views

### find the planar curve that passes two given points, whose tangent directions at these two points are also given

This is related to drawing the links and joints of a robot manipulator. I'd like to find a way to generate a link bwtween two given bars (joints), and the said link has to be normal to the two bars ...
39 views

### Plotting ellipsoid with coordinate axis

I would like to visualize the difference in coordinate shift for the ellipsoid using Mathematica. The above is a screenshot from wikipedia. What I need is to visualise the difference between ...
70 views

### Two different results for the same differential equation while using “AccuracyGoal”, “WorkingPrecision” and “PrecisionGoal”

I saw some strange behavior as I was solving a differential equation, so I decided to plot the solution in three different conditions. First, I defined the initial conditions and some constants: ...
115 views

### Two different solutions for the same ContourPlot while using AccuracyGoal and WorkingPrecission

I was making a contour plot, of some differential equation however I get two different solutions If I use "AccuracyGoal" and "Working Precision". The question will appear long but ...
51 views

### Integrating Superposition of several sinusoidal waves squared times its derivative

I'm currently finishing some research from a internship I did last summer and part of the project involves calculating the centroids of coronal holes from synoptic maps. If you aren't aware of what ...
51 views

### Density Plot on a Parametric Plot 3D

I am trying to insert a density plot on a parametric plot in 3D, but I am not successful. I post the part of the code on which I am working on. ...
135 views

### How do I fill last 'side' of this parametric plot?

I have three curves defined by ...
61 views

### Make the initial condition of a differential equation a function. DSolve and ParametricNDSolve

I'm trying to do something with DSolve and after I want to translate the solution of the problem to "ParametricNDSolve", however I can't. This is the problem, I have a function, and a ...
61 views

### How to integrate ParametricNDSolve solution and solve for parameter based on integration result

I have a second-order ODE that depends on a parameter $\rho_0$. For a given $\rho_0$, I can use NDSolve or ParametricNDSolve to get the solution $y(r; \rho_0)$ very easily, but I want to solve for the ...
36 views

### Exponential Regression for Parametric Equations

I have a few fairly complex parametric equations that describe a linear-log 2D graph which is unable to be described simply (in non-parameterized format). For various ease of calculation purposes, ...
48 views

### Parametric Plot 3D: A curve and a surface plot together

I am new to Mathematica and I tried to make a superimposed plot of a curve on a half sphere and need help with some graphics. This is the code line that i used to generate the following graphs <...
129 views

### Use ParametricNDSolve to get derivative at roots

$\ddot{s} = \frac{\mathrm{Thrust}(t)}{m} - g$ $\dot{s}(0) = v_0$ $s(0) = s_0$ Where Thrust(t) is a piecewise interpolation function. I want to obtain a function which gives me the maximum ...
33 views

### How to plot parametric phase diagram with bar legend? [closed]

I am trying to plot the parametric phase diagram with bar legend in the form of a rainbow. I have asked one similar question before in which I have shown the region plot. But equations are different ...
18 views

### How to impose periodicity conditions on some variables?

I have a quantity ds2 which is expressed in term of a set of 5 variables (let's call them t, r, θ, φ, ψ). I have 5 equations (...
82 views

### How to labels for each point in a list of arbitrary length?

I am attempting to illustrate a mapping from an isoparametric space to a parent (x-y) space for a variety of finite element types. Here we consider the simplest case of a three noded triangular ...
50 views

### Parametric NDSolve

I have to solve a differential system for different parameters and variable initial conditions. I have for example a system like this ...
100 views

### Parametric Volume

How can one write a function VolumeParametricPlot achieving the effect of a ParametricPlot3D with three parametrising variables, ...
81 views

### ParametricPlot returns empty output [closed]

I'm trying to generate the phase portrait for this differential equation equation: $(1+my^2)(d^2y/dx^2)+my(dy/dx)^2+y+1.1y^3$ Where y = 6, dy/dx = 0; m = 0.55. The plot is for x between 0 and 15 (...
20 views

### RegionPlot[ParametricRegion[···]] failing to generate output with simple rescaling of axes: ParametricRegion[···] cannot be automatically discretized

I'm trying to plot the image of a subset $U\subset \mathbb R^n$ under a map $F\colon \mathbb R^n\to \mathbb R^2$. Here is a piece of code which does the job in a simple case where $F$ is the identity ...
42 views

### How to get a method used by ParametricNDSolve?

How to get a method used by ParametricNDSolve for solving a problem? Specifically, a boundary value problem. The code looks like that: ...
115 views

### Getting errors in NonlinearModelFit

I need to fit a system of ODEs to data. The solutions which could work for me are given in the following posts How to fit 3 data sets to a model of 4 differential equations? ODE fitting to dataset ...
59 views

### RegionPlot with four parameters

I will try to illustrate my question with an example: Let us define the RegionPlot for b and ...
91 views

### How to divide a region in FEM with a parametric curve?

I'm using NDSolve with finite element to try to solve a heat transfer problem. The region I have is a rectangle where the four vertices are at ...
50 views

### How to use output of NSolve for further calculation and than plot?

I am trying to plot the output using these linear equations but finding some difficulty. Here I am using the output of these linear equations and after that using them in another formula and after ...
38 views

### Assign variable to solve [duplicate]

I would like to assign my result from equation. I tried /. and := but it gives me empty variable. How can i fix it?
47 views

### Having trouble drawing a llama using a Fourier transform in Mathematica. Works fine in p5.js, though

I am trying to draw llamas with the discrete Fourier transform on sample complex points of an SVG image of a llama. In my Javascript code (using the p5js. library) I sample points from the SVG and ...
134 views

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### How to plot root of the complex equations

I want to plot the roots of the complex equation of a1. I have tried the following code but this is not giving me any result. I need bistable plot. How it is possible.? ...
42 views

### How to plot parametric time dependent plot with different parameters taking average of time?

I am trying to plot the solution given in the code with respect to "delc". Now the problem is that it can be plot for a particular value of "t" like t=10,20,50,60,.. upto 100 but what i need is mean ...
62 views

### How to iterate a function

I have written a custom function called f1[r_] and I have tried iterating this function using Table. I work nicely for the first ...