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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5
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5answers
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 ...
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0answers
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: ...
2
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3answers
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. ...
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1answer
46 views

How can I plot Trajectory of 3d parametric plot?

x1 and y1 are constants. I have plotted ParametricPlot3D. ...
1
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2answers
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], ...
3
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2answers
128 views

Problem with FindFormula for experimental dataset [closed]

I have a dataset whose mathematical model is unknown. There is my code. ...
0
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1answer
82 views

Combine different kinds of plots [duplicate]

how can i combine thats plots: ...
0
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1answer
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?
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0answers
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 ...
8
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1answer
268 views

Calculate Radius of Curvature

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 ...
0
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1answer
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 ...
0
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1answer
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 ...
0
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0answers
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 ...
2
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1answer
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: ...
3
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2answers
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 ...
1
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1answer
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 ...
0
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1answer
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. ...
3
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2answers
135 views

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

I have three curves defined by ...
1
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2answers
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 ...
0
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0answers
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 ...
0
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1answer
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, ...
1
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1answer
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 <...
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0answers
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 ...
0
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1answer
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 ...
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0answers
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 (...
3
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2answers
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 ...
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0answers
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 ...
3
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2answers
100 views

Parametric Volume

How can one write a function VolumeParametricPlot achieving the effect of a ParametricPlot3D with three parametrising variables, ...
2
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1answer
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[0] = 6, dy/dx = 0; m = 0.55. The plot is for x between 0 and 15 (...
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0answers
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 ...
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0answers
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: ...
5
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1answer
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 ...
1
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1answer
59 views

RegionPlot with four parameters

I will try to illustrate my question with an example: Let us define the RegionPlot for b and ...
3
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1answer
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 ...
1
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1answer
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 ...
0
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1answer
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?
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0answers
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 ...
2
votes
3answers
134 views

Solve / brute-force for parameters that drive a function to zero at specified points

Edit: Made question a lot easier to read. Simple example. - Consider $p(x,y,z,t) = e^t(ax^2 + by^2 + cz^2)$ and I seek the values of $a,b,c$ which make $p\approx0$ at the point $(x=r\cos\theta,y=r\...
0
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1answer
46 views

Finding an instance of a parametric equation that intersects given points

So I have this equation for a circle centered at the origin that has some orientation in 3D space. ...
0
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0answers
20 views

Find the curvature circle tangent to a space curve [duplicate]

I'm trying to find the circle with curvature radius tangent to a space curve, like $\vec{s}(t) = [\cos{t}, \sin{t}, \frac{t}{5}]$. I notice that the circle lives on the plane the velocity and ...
6
votes
1answer
184 views

Solve can't solve my trigonometric equation—why?

I have the following equation for epsilon $2 |\alpha_{n,ch}|=\epsilon+\cos^{-1}(\tan(\frac{\pi}{4}-\frac{\epsilon}{2}))$, where $\alpha_{n,ch}$ is a negative constant (e.g. -0.769) I tried to solve ...
0
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2answers
54 views

Making the solutions of a ParametricNDSolveValue show up as different colours?

I am having a bit of trouble when it comes to plotting the solution of a system of non-linear ODE's. I write ...
1
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1answer
38 views

Solving 3D system of equations with two algebraic eqs. and one parametric? [closed]

I'm trying to find a way to compute all solutions to system of three equations. Two of them are usuall algebraic equations, and third one is a parametric equation. Is there any way, to for example ...
2
votes
1answer
64 views

ParametricPlot Incomplete

I have a problem to reproduce a graph. Follows the commands used: ...
1
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1answer
78 views

Plot Arc Length Parametrization

I want to plot the parametrization of the curve with respect to arc length. It is all known that we have to find the inverse of the arc length of the original function i.e. $F(t)$, and ...
1
vote
1answer
112 views

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.? ...
0
votes
1answer
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 ...
1
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0answers
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 ...
2
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1answer
186 views

Need help solving ODE with ParametricNDSolveValue solver

I am trying to apply @bbgodfrey method for finding the right initial guess for the following problem but I get an error message and I don't understand where it comes from. I would also like to ...
2
votes
1answer
47 views

Parametric Plot of Simultaneous Equations

I have tried to solve a pair of simultaneous equations in Mathematica. I was able to solve these equations but I was unable to plot them in the way I wanted. My equations gave me solutions for two ...

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