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21
votes
5answers
851 views

Fitting points to tilted, off-center ellipse

I have 24 x-y points that are supposed to form an ellipse. ...
20
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 ...
18
votes
2answers
903 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?
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 ...
10
votes
5answers
907 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? ...
8
votes
2answers
774 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 ...
7
votes
5answers
1k views

Filling between parametric plots

I am new with Mathematica, but am trying to fill an area between two parametric plots ...
5
votes
3answers
455 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: ...
4
votes
2answers
323 views

Intersection of Osculating Circle with a Parametric Curve

I have the following Parametric plot Generated from the following: ...
4
votes
2answers
285 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 ...
4
votes
3answers
151 views

I need to remove a line from a ParametricPlot

What happens is that when I make this ParametricPlot: ...
4
votes
1answer
194 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 ...
4
votes
1answer
579 views

Plotting a 2D shape along a 3D parametric function curve

Say I have a 3D curve that is parametrically defined. How would I be able to plot shapes like figure 8s whose centers are aligned along the 3D curve? Say the curve was: ...
3
votes
1answer
147 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 ...
3
votes
1answer
192 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: ...
3
votes
1answer
581 views

Normal and Tangent of Acceleration in 3D

I need to figure out how 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 ...
2
votes
3answers
233 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 ...
2
votes
1answer
411 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
4answers
313 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 ...
2
votes
2answers
107 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 ...
2
votes
1answer
534 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
votes
1answer
168 views

ParametricPlot3D[] Question

I know this is very similar to a previous question I asked, but there are some differences. When I graph: ...
2
votes
1answer
284 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? ...
2
votes
1answer
268 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 ...
2
votes
1answer
77 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 ...
2
votes
1answer
221 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 ...
1
vote
3answers
213 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 ...
1
vote
3answers
106 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 ...
1
vote
3answers
198 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
vote
2answers
384 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
2answers
699 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 ...
1
vote
2answers
134 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) ...
1
vote
2answers
162 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
166 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
1answer
69 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. ...
1
vote
2answers
217 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
1answer
134 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 ...
1
vote
1answer
182 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 ...
1
vote
1answer
233 views

Unable to solve a set of equations with Solve

I'm trying to solve the following equation using Mathematica 9.0.1.0 : ...
0
votes
1answer
148 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 $t$?
0
votes
3answers
75 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 ...
0
votes
1answer
115 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 ...
0
votes
1answer
86 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 ...
0
votes
1answer
146 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
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
93 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? ...
0
votes
2answers
212 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 ...
0
votes
1answer
65 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 ...
0
votes
1answer
122 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 ...