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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2
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1answer
79 views

Empty graph when using parametric plot 3D

I want to plot a parametric 3D plot from the following ParametricNDSolve code: ...
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2answers
71 views

How to simplify this sum of random waves?

Is there a way to simplify the random functions and their calls, in the code below? ...
2
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1answer
128 views

How to make this moving surface a continuous and derivable function?

I'm having troubles in defining a function of three variables: $t$, $x$, $y$, from a moving bumpy surface that should be derivable relative to its three variables. Here's the animated surface code, ...
1
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1answer
76 views

Randomly oscillating surface is not working well

I'm trying to built some random moving surface from a plane perturbed with random oscillators, and my current code isn't doing what I need yet, as seen from the ...
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1answer
48 views

I have a function $R \to C$, I want to plot it as the way we can plot parametric equations in the $R^2$. How to do it?

I have a real variable $t$ and a function $f(t)$ giving complex values. How to plot the function for $t$ in a given real interval? Also is there a way to do it in Wolfram Alpha website?
2
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1answer
49 views

How to insert variable height in this random bumps function?

I'm trying to insert a "time" variable that control the height of the random smooth bumps, but I'm yet unable to do it right, as shown with the code below: ...
2
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2answers
48 views

How to find maximum of two or more parametric functions?

I have two parametric functions in which I know the range of parameters and I want to find the maximum of these two functions by conditions on the value of the variable. Suppose $f(x)=x-c$ and $g(x)=r....
1
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1answer
38 views

Plotting ParametricNDSolve Value

I am trying to solve a set of coupled differential equations, where I would create plots for a(t) and e(t), where the parameter RAST can be varied. However, every time I try to plot, I get blank plots....
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2answers
107 views

ParametricPlot3D as a ContourPlot

I want to plot the amplitude of a complex-valued function of one complex variable. I want to do this in the plane defined by the real and imaginary parts of the complex variable as a ...
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1answer
81 views

How to solve the Summation equation by FindRoots [closed]

I want to find out the value of alpha and lambda where u lies between 0 and 1.
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0answers
113 views

Plot the Corner Control Points

I face some problem of plotting the control points at the corner. I only want to plot the control points at the corner only. I do not know how to plot the corner control points from all the control ...
3
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2answers
153 views

Plot3D Equation of motion of a particle in a surface

I'm new in this forum. This semester I've been trying to learn how to use Mathematica for my Classical Mechanics course, but I'm still a novice concerning this software. In particular today I was ...
5
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2answers
292 views

Using fewer mesh lines, 3D graphics

I want to make the Final use fewer mesh lines, the ideal version will look like the second image. Where the triangle shape is more clear and clean. Can anyone give me some advice on how to fix my code?...
2
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1answer
67 views

How &@ and &/@works?

I have the following expression: (Join[#, Reverse[#, {2}]] &@Partition[#, 2, 1, 1]) & /@ Vec (* where: *) Vec={{2,0},{1,1},{0,2}}, but I am not sure how ...
2
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2answers
75 views

control net of the torus

I want to make a complete control net of a torus. However, the net is not closed. Can anyone solve this problem? ...
0
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1answer
66 views

Solve system of 5 unknowns and 5 nonlinear equations

I attached below the system of 5 equations that I am not able to solve using FindRoot. I also tried without defining the equations as functions but It didn't work. ` ...
0
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0answers
51 views

Animate ellipse drawing

$(x/3)^2+(y/5)^2=1$, $x=3\sin[t]$, $y=5 \cos[t]$ I want to draw a phase trajectory with time-lapse using manipulate or animate. Manipulate[ParametricPlot[(x/3)^2 + (p/5)^2 == 1, {x, -3, 3}, {p, -5, 5}]...
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2answers
47 views

How to Solve a function f[x[y],y] == 0 in Mathematica? i.e. a function of 2 variables, where one is dependent on other

I am new to Mathematica and am trying to solve an equation to calculate amplitude as a function of frequency numerically. The parameters are as follows :- ...
3
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3answers
122 views

Equipotential surfaces using ParametricPlot

So I'm trying to plot lines on which the following function is a constant $$ \frac{\left(-\Sigma (r,0.99,\theta )+2 r^2-0.99^2 r \sin ^2(\theta )\right)^2}{\Delta (r,1,0.99) \Sigma (r,0.99,\theta )^3}+...
1
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1answer
60 views

expand function as power series of another function

Suppose I have a well-known function $f(x)$ and I want to know if this function can be expanded into power series of another function $g(x)$, like $f(x)=\sum_n a_n g^n(x)$, where $a_n$ is the ...
0
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1answer
45 views

Not respected assumptions

I' m writing a function with the following line: ...
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0answers
30 views

Minimize doesn't work with more parameters

In the code I wrote there is a ParametricNDSolve with four parameters. I want to minimize an error function with Minimize. If I consider ParametricNDSolve with just one parameter everything works, and ...
2
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2answers
70 views

Is there a way to an implicit equation into parametric form?

For example, take the implicit equation for the unit circle $\qquad x^2 + y^2 = 1$. Is there a function Parameterize[x^2 + y^2 == 1] that would return a vector ...
0
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1answer
117 views

How can I solve this Integral?

I have a two variables function. I have to numerically or parametric integrate this function with respect to one of the variables (\tau) and assume the other variable (t) is constant. Note, however, ...
2
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1answer
71 views

How can I fill in a section of an ellipse converging on a focus rather than the center?

I am trying to plot a simple display of Kepler's second law - equal areas of an ellipse swept out in an equal amount of time. The problem is that I need my sections area sections to have a focus as ...
2
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1answer
74 views

A doubt on ParametricPlot3D, RevolutionPlot3D, ListPlots and NIntegrate: can I build an “RevolutionListPlot3D”?

First of all: this is question lies in the context of Surfaces and Embbedings on differential geometry. More precisely in the context of Kruskal coordinates and how to plot a 3D dynamical ...
0
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1answer
29 views

How to calculate Sum of a function over a list

tlist = Table[i, {i, 1, 10}] tlist:{1, 2, 3, 4, 5, 6, 7, 8, 9, 10} f = E^(-((2 t)/T)); ...
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0answers
28 views

Using NonlinearModelFit from ParametricNDSolveValue with three parameters

Here is the very desired Parametricfunction , calculated using ParametricNDSolve, from physical arguments. From this, an interpolating function dens is settled. ...
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0answers
44 views

Find parameter ranges of a function whose value is within a window by sampling points

Problem: I want to find the ranges of the parameters for a function $f(x,y,z)$ when $0.9 < f(x,y,z) < 1.1$. All parameters are bounded $x , y, z \in [0,1]$. In the real problem the function ...
0
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0answers
18 views

Assign multiple parameters after function evaluation

I want to conduct sensitivity analysis on an ODE (say with two independent variables x,y) with many parameters. The issue I have boils down to trying to do it all at once in a module. My attempt ...
0
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0answers
41 views

generating a Poisson Gap sampled schedule

I have a grid of 256 points (0,1,....M-1), which I then want to distribute in sinusoid weighted Poisson Gap. tpts = Table[t, {t, 0, 255}]; I define two functions ...
1
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2answers
92 views

Best way to solve stupidly complicated parametric non linear equation with reduce/solve etc

I have a parametric nonlinear function which is literally a nightmare. I know roots exist, they are real and the two parameters, p,e are both positive. What I was ...
8
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3answers
350 views

Finding the Period of a Limit Cycle

I'm interested in the periods of limit cycles of the Wilson-Cowan equations which have the form $$x'(t) = -x + S(ax(t) - by(t) +e)$$ $$y'(t) = -y + S(cx(t) - dy(t) + f)$$ where $$S(x) = 1 + \frac{...
6
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5answers
346 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 ...
2
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3answers
78 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. ...
0
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1answer
54 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
66 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
152 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
92 views

Combine different kinds of plots [duplicate]

how can i combine thats plots: ...
0
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1answer
36 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
129 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
314 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
50 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
32 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
52 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
78 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
125 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
67 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
76 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
138 views

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

I have three curves defined by ...

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