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24
votes
4answers
3k 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 ...
1
vote
0answers
73 views

Plotting knot torus

I'd like to plot together a torus and a knot on it, that is, closed curve wrapping around the torus, $m$ times around a circle and $n$ times around the other circle. It will be used to explain ...
2
votes
2answers
106 views

cycloid parametric [closed]

How do I enter 3 parametric equations for cycloids corresponding to circles with radii 1, 2, and 4. I have tried ...
0
votes
1answer
62 views

Simplify trigonometric equation knowing that $sin(a)=n*sin(b)$

I was working on a problem involving trigonometry. I used Mathematica to help me in solving it. I ended up with this formula: ...
4
votes
4answers
501 views

Visualizing Line Integrals

I have a plane curve $C$ described by parametric equations $x(t)$ and $y(t)$ and a function $f: \mathbb{R}^2 \rightarrow \mathbb{R}$. The line integral of $f$ along $C$ is the area of the "fence" ...
7
votes
1answer
301 views

Oval or Bunimovich stadium

The dynamic billiard demonstration, that can be found on wolfram demonstrations (here), is only designed for an ellipsoid-shape boundary(snapshot below). The idea is to have a dynamic billiard with ...
0
votes
1answer
55 views

RegionPlot Difficulty

This code: Plot3D[ArcTan[Tan[y/x]], {x, -1, 2}, {y, -2, 1}, RegionFunction -> Function[{x, y}, 1 <= x^2 + y^2 <= 4 && y <= x]] Give this ...
1
vote
2answers
135 views

How can I plot a 3-variables function to identify the neutral surface and a region

I wanted to plot a 3-D solid region, in which my function f(x,y,z)= x (1/(1 + 0.06))^3 + y (1/(1 + 0.06))^2 + (2 z^2)/15 (Sin[10 Degree])^2 -z/3 Cos[10 Degree] ...
1
vote
1answer
80 views

Filling between ParametricPlot and Plot

There are some similar questions: (1) (2) have been ask, but I think this is a different one. If we have a ParametricPlot and a ...
0
votes
0answers
32 views
1
vote
2answers
202 views

Eliminating the Parameter: Transform parametric equation to Cartesian equation and draw arrows along parametric growth

Hey guys I really could use some help on this calc 3 problem. I'm stuck on how to write the code for this problem: a) Eliminate the parameter to find a Cartesian equation for a parametric curve. b) ...
0
votes
1answer
92 views

PolarPlot works, ParametricPlot doesn't

Am new to Mathematica, so if this question has been asked already, apologies. Have a (polar) spline function and Mathematica did a fine job of calculating from my inputs and giving me the piecewise ...
4
votes
2answers
347 views
4
votes
3answers
161 views

I need to remove a line from a ParametricPlot

What happens is that when I make this ParametricPlot: ...
2
votes
1answer
433 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 ...
2
votes
3answers
252 views

How can I get the function of a plotted trajectory? [closed]

I solved two ODEs, which are a function of t, numerically. The first ODE is the vertical equation of motion and the second one is the horizontal equation of that ...
1
vote
1answer
75 views

FindRoot error, Solving equations [closed]

I'm trying to solve this problem but FindRoot function seem unable to find the root when r equals 4. ...
0
votes
3answers
79 views

Parametric Equation with restrictions on the independent variable [closed]

I'm sorry if this question was answered but I am completely new to Mathematica, really learning as I go (background in Java). The questions I looked at that were suggested didn't make much sense with ...
2
votes
1answer
91 views

Piecewise conditions with a parametric PDE

I'm using ParametricNDsolve to check best fit of a model (function Eb1) with some data, and I have four free parameters I want to test. I can easily construct a Parametric solution between the two ...
1
vote
1answer
65 views

Density plot of asymptotic behaviour of a linear system

Good morning, I have an ODE linear system $\dot{\vec f} = A \vec f$ depending parametrically to two real parameters, s and p. I'd like to get a density map of the solutions of $f_A/(f_A+f_B)$ at ...
0
votes
0answers
42 views

Pass model parameters to NDSolve'Reinitialize

I am wondering if there is a way to pass parameter values during the NDSolve'Reinitialize step of the NDSolve process? I've read that one way to possibly speed up repeated calls to NDSolve is to ...
22
votes
5answers
944 views
2
votes
3answers
259 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 ...
3
votes
1answer
150 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 ...
2
votes
2answers
110 views

Finding the intersection of curves in a one-parameter family [closed]

I have a function f[c_] := y^2 - 2 x^2 (x + 3) == c ((y + 1)^2 (y + 9) - x^2) I need to find the points of intersection between the plots of f[0] and f[2]. How ...
0
votes
0answers
52 views

Plotting surfaces described by redundant variables - Alternatives to use of Eliminate + ContourPlot3D

Suppose I want to plot a surface defined by equations involving redundant variables. Consider, for example, plotting the surface defined by the equations: $$ \left\{ \begin{array}{l} \cos x + \sin y = ...
4
votes
1answer
205 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 ...
0
votes
1answer
216 views

How to the take derivatives of a parametric function? [closed]

I have a parametric curve of the form $x(t)=2t^3+3t^2-12t,\ y(t)=2t^3+3t^2+1$ How do I take the derivative of that function in Mathematica? Is there a certain function I should use?
0
votes
1answer
68 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 ...
1
vote
2answers
243 views

Parametric 3D plot with parameters satisfying an implicit equation

I am trying to plot a function $ {\bf x}(t) = r(t)\hat{v} + {\bf b}(t) $, with unit vector $ \hat{v} $ and vector $ {\bf b}(t) $ given in spherical coordinates. For simplicity, assume that $ \hat{v} = ...
1
vote
2answers
176 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 ...
1
vote
1answer
200 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 ...
1
vote
3answers
225 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 ...
0
votes
1answer
158 views

Solving parametric equations by eliminating the common variable [closed]

I'm trying to solve simple parametric equations using mathematica, but I'm having trouble finding a function to do this... what is the simplest way to solve for a common variable? For example, I have ...
1
vote
1answer
140 views
17
votes
4answers
2k 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 ...
0
votes
0answers
106 views

How to solve a ParametricNDSolve issue when the system seems to be stiff?

I have a problem with ParametricNDSolve[]. Mathematica gives the warning that a stiff system is suspected. I have varied the methods but unfortunately I was not ...
1
vote
3answers
108 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 ...
0
votes
1answer
161 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: ...
2
votes
1answer
583 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 ...
0
votes
1answer
55 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 ...
0
votes
2answers
94 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
vote
1answer
277 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
votes
1answer
299 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? ...
0
votes
1answer
203 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 $t$?
20
votes
2answers
991 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?
1
vote
2answers
443 views

ParametricPlot3D with three variables

ParametricPlot3D can be used with one or two variables to plot paths and surfaces in 3-D such as ...
1
vote
1answer
217 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 ...