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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16
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4answers
2k views

How to create these famous surfaces in topology with the desired color effects?

It was said such real objects of famous topological surfaces were plotted by the cooperation between mathematician Richard Palais and artist Luc Benard, and published as the cover page of Science ...
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3answers
1k views

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 ...
5
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1answer
384 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 ...
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1answer
146 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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2answers
545 views

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 ...
2
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1answer
1k views

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 ...
2
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3answers
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 ...
1
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1answer
221 views

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 ...
4
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1answer
361 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 ...
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3answers
153 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 ...
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1answer
486 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: ...
0
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1answer
82 views

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 ...
2
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2answers
231 views

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? ...
1
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1answer
585 views

Unable to solve a set of equations with Solve

I'm trying to solve the following equation using Mathematica 9.0.1.0 : ...
2
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1answer
694 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? ...
3
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1answer
1k views

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 ...
0
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1answer
1k views

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 $t$?
23
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2answers
4k views

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?
9
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2answers
3k views

ParametricPlot3D with three variables

ParametricPlot3D can be used with one or two variables to plot paths and surfaces in 3-D such as ...
28
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6answers
8k views

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 ...
1
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1answer
915 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 ...
4
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2answers
1k views

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 ...
0
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2answers
890 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 ...
2
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1answer
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 ...
2
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1answer
462 views

ParametricPlot3D[] Question

I know this is very similar to a previous question I asked, but there are some differences. When I graph: ...
49
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5answers
24k 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 ...
12
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6answers
6k views

Filling between parametric plots

I am new with Mathematica, but am trying to fill an area between two parametric plots ...
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1answer
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 ...
3
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1answer
473 views

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: ...
0
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2answers
316 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 ...
3
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1answer
944 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 ...
3
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1answer
2k views

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 ...
0
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0answers
170 views

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 ...
5
votes
3answers
1k views

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: ...
3
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1answer
814 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 ...
5
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4answers
892 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 ...
18
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6answers
3k views

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? ...
1
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2answers
4k views

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 ...
8
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2answers
2k views

Find the parameter values satisfying conditions for all roots of an equation

Hi I'm very new at Mathematica. My real problems concerns a much more difficult equation with many parameters, but I want to check that the method is good, so I made up a test equation. My test ...

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