# 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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### Marking specific points on a 3D curve

Here is the curve below. (written as a position vector) r = {Cos[7 Pi*t], Cos[6.2*Pi*t], 2.5*t} ParametricPlot3D[r, {t, 0, 2}] I want to know how I can mark ...
394 views

### Partial zeta curlicues

I asked a question at MSE and Raymond Manzoni provided an excellent answer that included these visuals: I made a very basic attempt at recreation with ...
148 views

### Define function that goes from one point to another parametrically

I have two points p1 and p2, and I want to get the parametric equation of a linear function that passes through those, but ranging from one point to another. For example, if I have 2 points {0,0} and ...
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### Manipulate wrapping ParametricPlot3D - part spec longer than depth of object?

I have a system of parametric equations s0 = {t0, 0. +2. Sin[θ] Sin[ϕ]-1. (0.5 t0+0.5 Sin[θ] Sin[ϕ]), 4. (0. +0.25 Cos[θ] Sin[ϕ]), 1. Cos[ϕ]} If I plot them ...
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### Can ParametricNDsolve be used for coupled PDEs with 5 parameters?

I have a system of coupled PDEs with five parameters that I only know ranges for rather than explicit values, and I was wondering if I could define a parametric equation with ParametricNDSolve and ...
2k views

### Plot parametric solutions using Manipulate [duplicate]

I want to plot the parametric diagram of {y[t],z[t]}, in which I manipulate a parameter, ω, from $[1, 10 \pi]$. Here is what I have attempted, but I can't get a ...
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### invert system of two parametric ODEs and plot results of do-loop

I can solve this system of parametric ODE (u is the parameter,while g,e and ...
366 views

### Changing Plot order for 3D printing

Alright, I got a my first 3D print done of a pseudosphere using parametric plot and a deflated sphere using a contour plot, but when I try ...
155 views

### Difficult parametric function

I've got this strange parametric function and I want to implement it on Mathematica. I know that I could use Excel and calculate it, but my database is quite large and I want to do some reproducible ...
502 views

### Plotting discrete points on a phase plot

I'm trying to generate a phase plot of a sinusoidal voltage at discrete points using the following code: ...
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### Find all values of the paramaters $m$ for which the equation has four roots smaller 2

I want to find all values of the paramaters $m$ for which the equation $$t^4 + (2 m - 1) t^2 - 18 m - 72=0$$ has four real distinct solutions less than 2. Put $t = x^2$, I tried ...
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### Sum equation with equation and get an equation

I am trying to get an equation from summing other equations but it doesn't result in a correct answer. Is there another way of doing this? ...
590 views

### Unable to solve a set of equations with Solve

I'm trying to solve the following equation using Mathematica 9.0.1.0 : ...
706 views

### Speeding up solving a system of simultaneous equations

I am trying to solve the following system of equations. Solve takes a very long time to solve the following system of equations. Is there any way to speed it up? ...
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### Interpolate a curve in 3D

I have a sequence $\{(x_k, y_k, z_k)\}_{k=1}^n \subset \mathbb{R}^3$, all points along a path represented by the function $\gamma \colon \mathbb{R} \to \mathbb{R}^3$, which maps the distance along the ...
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### How do you express a function of x,y,and z as a function of the parameter t in a vector?

If I have a vector say for example $\vec{r}(t)=<t,t^2,3t^2>$ and a function $f(x,y,z)=\sqrt{1+30x^2+10y}$ whats the best way to express $f(x,y,z)$ as a function of the parameter $t$?
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### How to plot a certain surface? What is its parametric equation?

The surface show below is very beautiful; however, I don't know its function either as an implicit function or in parametric form. Anyone have an idea about it and how to draw it with Mathematica?
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### ParametricPlot3D with three variables

ParametricPlot3D can be used with one or two variables to plot paths and surfaces in 3-D such as ...
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### How to get intersection values from a parametric graph?

I have this graphed: ParametricPlot[{2.4*Cos[t] + 1.6*Cos[3 t/2], 2.4*Sin[t] - 1.6 Sin[3 t/2]}, {t, 0, 4*Pi}] It is a star, and the lines cross each other twice ...
938 views

### Using ParametricNDSolveValue with initial conditions of another ParametricNDSolveValue

I have a system of parameter-dependent ODEs, which I can solve using ParametricNDSolveValue. Now, I have another ODE, which has as initial condition the solution of ...
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### Find the value of parameter so that the equation has one solution

Let $(E_l) : x^4-4x^3+x^2(5-l^2)+4 x l^2-4l^2 = 0$ be an equation with $l$ as a parameter and $x$ as an unknown and $S_l$ the set containing all the real solutions of $(E_l)$. Then there is a unique ...
891 views

### Plotting problem

I was wondering why I keep receiving the error message "Derivative should be a triple of numbers, or scaled form" from the following code ...
2k views

### Nonlinear least squares

I have a typical nonlinear least square problem and it seems very similar to the example provided in the section on parameter fitting at the Wolfram website. Unfortunately I always get some error ...
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### ParametricPlot3D[] Question

I know this is very similar to a previous question I asked, but there are some differences. When I graph: ...
25k views

### Find eigen energies of time-independent Schrödinger equation

I'm trying to get the eigenvalues of a one dimensional time-independent Schrödinger equation, $-\frac{h^2}{2m_0}\frac{d^2\psi}{dx^2}+U(x)~\psi=Ei~\psi$ where U(x) is some potential and Ei is the ...
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### Filling between parametric plots

I am new with Mathematica, but am trying to fill an area between two parametric plots ...
158 views

### ParametricPlot Question

I want to graph more than two, lets say 5 different ParametricPlot-s all in terms of different time variables. Is there any way to do this, such that they all show ...
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### ParametricNDSolve and Constraint satisfaction problem

I am trying to find the values of two parameters that allow for a specific result of my differential equations, under different initial conditions. Given a system of equations: ...
322 views

### Interpolating a ParametricFunction

Original domain of my independent variable t is 0 to 10 nanometers, but in Mathematica (as in most numerical software), it's good idea to solve differential ...
947 views

### Limitations of ParametricNDSolve family w.r.t objective functions

Observation: I can see even for very simple modification in case of an scalar objective involving an definite integral in time ParametricNDSolve fails. Here is an ...
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### Normal and Tangent of Acceleration in 3D

I am trying to find the normal and tangent of acceleration. I know the formula for the tangent of acceleration is $((Acceleration . Velocity)/(Velocity.Velocity))*Velocity$ and the normal of ...
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### Is there a way to add arrows along a parametric curve inside a manipulate function? [duplicate]

I cannot find a good way to add arrows along a parametric curve that I used NDSolve to get. I have written everything inside ...
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### Solve for the intersection point of 3 surfaces

Basically, I have three 2-torus (tilted) in 3-dimensional Euclidean space. They are expressed by parametric equations: ...
844 views

### How to integrate ParametricNDSolve solution with respect to a parameter?

I have just upgraded to the new version of Mathematica because of its new built-in ParametricNDSolve function. I need to solve a first-order non-linear ordinary ...
933 views

### Problem with WhenEvent

I am trying to add a time dependent fraction to a parameter in NDSolve, i.e. when 10 < t< 20, add ...
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### How do I obtain the enclosed area of this particular parametric plot?

I'm trying to find a way to obtain the enclosed area of this particular plot. Can someone show me how? ...
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### Parametric plot from two NDsolve solutions

I have two independent ODE systems. A = NDsolve[..., {x, y}, {t, 0, 10}]; B = NDsolve[..., {a, b}, {t, 0, 10}]; I can draw a ...