# 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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39 views

### Facing problem using NSolve inside module

I have an equation called P, which is a determinant of the matrix R. This equation P is a function of ...
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### Export Graphics3D Object as .fbx file with animation

Suppose I have a Graphics3D object named objanim that is a function of some variable t. I can export this animation to a ...
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### How to specify in Parametric Plot that variables are on circle?

I have 2 functions a=2; zx[x_, y_] := x + (a^2*x)/(x^2 + y^2); zy[x_, y_] := y - (a^2*y)/(x^2 + y^2); I want to draw a parametric plot of (zx,zy). Where x and y ...
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### Plot of Parametric Equation that describes a Lead Screw

I have a Lead Screw, it looks like this: There are two parameters at the moment of buying one: Pitch and Lead The Lead Screw that I have has a Lead of 2mm and a Pitch of 2mm, but I find a little bit ...
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### How do I define a function with a variable and a parameter? [closed]

Let $\alpha \in (0,1)$ be a parameter. I would like to define a function $$f_{\alpha}(n) := \binom{n}{\alpha n},$$ in order to later get a series expansion ...
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### How do I plot a parametric function? [closed]

I want to plot this parametric function: $\qquad x=2\,\cos(\sqrt{12}t- π/3),\,y=4/\sqrt3 \sin(\sqrt{12}t- π/3)$ where $t$ goes from 0 to 8 I tried to make a plot, but I didn't know how because it's ...
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### Can we convert any parametric equation to implicit form?

The Archimedes spiral equation in parametric form: fx[t_] := Cos[t]*t; fy[t_] := Sin[t]*t; How can it be converted to implicit form? Is there a general method ...
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### Allow Mathematica to solve the differential equations with larger than 16 digits parameters

Consider the system of differential equations ...
131 views

### How to plot a super ellipse [closed]

I am trying to plot a super ellipse. It's like a regular ellipse but there are added terms so you can define how box like the ellipse will be and on the other extreme how concave the shape will be. I ...
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### How to draw a 3D point moving along a helical path?

I have an animation for a helix being drawn in 3D but I really want to have a point on there that draws the helix. I've seen similar problems on here for 2D and I tried adapting the suggestions but I ...
164 views

### Need help on working with parametric function

Here is an ODE solved by ParametricNDSolveValue solver.I got the solution. Now, I need to solve these two equations: p1 = 10 h - l; p2 = 10 h1; where ...
84 views

### How to fit spline through points in $\mathbb{R^3}$?

I have coordinates of points that represent a curve (for example, helix or centerline of moebius strip) in $\mathbb{R^3}$. I want to fit a Bspline through these points. How to do this in Mathematica? ...
588 views

### return {} when the function is given {}

I have a function taking an array as argument and giving an output. However, sometimes my argument is {} (the empty array), then how can I get an output {} when my argument is {}? Actually, I want the ...
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### ParametricNDSolveValue vs NDSolveValue

My question is simple. If I define this system of differential equation with NDSolveValue I obtain a pretty result ...
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### Is function polymorphism possible in Mathematica [duplicate]

Is there a way to have polymorphic function definitions in Mathematica? I looked around online and didn't anything discussing it.
339 views

### Finding a parametric curve fitting a two-dimensional dataset

I have a 2-dimensional data set where I want to find the function that fits best the points. My issue is that I am looking for a function of the for $f(x,y)=c$ with $c$ a constant. I could not find in ...
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### Performance Optimizing ParametricFunction

Setting up the system: ...
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### Plotting the solutions of parametric NDSOLVE[] as a function of its parameters

I am trying to solve a 2 set of coupled differential equations one using parametricndsolve and other using *ndsolve . So far I am successful in solving these equations. The solution I found by using ...
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### ParametricPlot with condition for parameters

For example ParametricPlot[{Sin[x] - y, Cos[y] - x}, {x, -\[Pi], \[Pi]}, {y, -\[Pi], \[Pi]}] gives What should I do to impose ...
207 views

### Problem combining ParametricNDSolve with NonlinearModelFit

Final Edit: I have found a solution! Specifying Method->"LevenbergMarquardt", Gradient->"FiniteDifference" gives the behavior I am looking for. Huzzah! It appears that the crashing behavior was coming ...
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### Plotting an NDEigensystem solution over a helicoid

I am trying to plot the solutions of a particular Hamiltonian eigensystem over a helicoid. In other words, my solutions are a function of the radial variables (r,$\phi$). The Helicoid is given by the ...
80 views

### Parametric equation of rolling polygon (cyclogon)

Abraham Gadalla tried (but failed) to post the following question. Why does the red point not continue to follow the square (and the curve) for the full range $0\le x\le 2\pi$? ...
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### function application f//x when the function has more than one parameter [closed]

I want to use the function apply (or something even better). x//f with a function that has more than one parameter. Here is how it works with one parameter. <...
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### How to Plot modulo function Mod on a function of two variables? [closed]

I know that Plot[Mod[x, 2], {x, -6, 6}] is a Mathematica command to plot the remainder of x over 2 when I range x over reals -6 to 6. How do I plot the same ...
267 views

### How to derive trigonometric Cartesian equation from parametric

How can one derive programmatically a Cartesian equation when $x$ and $y$ are parametrically represented by trigonometric functions? i.e.: Given that $x= \cos(2 t)$, and $y = -\sin(t)$, how can I ...
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### Manipulating a ParametricFunction to handle units

I have a pretty nice way to handle units on a result from NDSolve, which basically consists of converting all of the units to SI, stripping them, calling NDSolve, and then putting the units back. I'll ...
89 views

### Blank graph on offline mathematica

I am looking at the following plot: ...
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### ParametricNDSolveValue with SparseArrays

I want to solve large, sparse matrix systems with ParametricNDSolveValue and was hoping to use SparseArray to speed up the computation. However I find that ParametricNDSolveValue doesn't seem to work ...
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### Issue with Manipulate (in order to fit) of complicated Parametric NDSolve

So I have a quite complicated ParametricNDSolve : ...
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### Fitting data points with a function obtained by ParametricNDSolve+Integrate

My question concerns fitting data points to a function that is a solution of a set of parametric differential equations, then integrated over time. More specifically, I have these parametric ...
29 views

### How to calculate function with Expectation , Max and Min ? Is my express is right or not?

I want to do the numerical analysis, here are the functions: i=1,2;j=1,2;"i" is not equal to "j". The following is my code:
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### Use ContourPlot data in ParametricPlot

Let me give an example, probe1 = ContourPlot[10 == x + y, {x, 0, 10}, {y, 0, 10}, Frame -> True, FrameLabel -> {"x", "y"}] This plots ...
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### Solution to non-algebraic equation with parameters

I have to solve the following equation a Tanh[z-b] = z, with a and b parameters and ...
315 views

### Best way to write an equation with subscripts and superscripts

This post is not about a specific Mathematica problem but about to develop the best way to enter mathematical equations with subscripts and superscripts. I have a ...
63 views

### How to list all the possible functions of given structure?

I can run this command : Tuples[{ Tuples[{x, y, z}, 2], {a, b, c}}] to list all combinations that looks like: ...