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14
votes
2answers
366 views

Symbolic area calculation for a parametric self-intersecting closed curve

The parametric equation of the curve is: $$\begin{cases} x &= -9 \sin (2 t)-5 \sin (3 t) \\[6pt] y & = 9 \cos (2 t)-5 \cos (3 t) \end{cases}\quad t\in[0,2\pi]$$ which can be easily ...
4
votes
2answers
157 views

How to obtain the area enclosed by such a curve?

The desired curve is defined as curve02 below : ...
3
votes
1answer
188 views

Using ParametricNDSolve and NMinimize to find accurate interplanetary trajectory arrival periapse radius

I have an interplanetary trajectory simulation that calculates the required velocity (using a Lambert solver) and escape angle for a spacecraft to travel from Earth to Mars. This model does not use a ...
6
votes
1answer
102 views

ParametricNDSolve[ ] and NMinimize[ ] in Combination

I have the following code that is used to simulate a spacecraft orbiting Mars, and uses ParametricNDSolve to vary the spacecraft's initial conditions using a parameter value ...
0
votes
3answers
69 views

Confusing “Part::pspec” and “Part::partw” following call to ParametricPlot3D

The problem I'm having is that the function definition given below continually gives me baffling error messages. I'm trying to turn a list of 3D points into a function that approximates a curve by ...
2
votes
1answer
95 views

Minkowski sum and product of 2D-regions

Let $A_j$, $j=1,\dots,n$ be subsets of $\mathbb C$ defined by $$ A_j=\{z\,|\,f_j(z)\geq0\} $$ where $f_j:\mathbb C\to\mathbb R$ are given functions. I am interested in the following subsets of ...
0
votes
0answers
24 views

Find Multi-variable intervals with given constraints in complicated expressions

I am working on finding variables' intervals that satisfy some conditions and subject to some relations. At first, these variables have intervals pre-defined as follows: $$0 < \alpha, \beta, ...
0
votes
0answers
34 views

ParametricNDSolve of differential equation with singularity

I have a differential equation I would like to solve with the ParametricNDSolve. However, the coefficients in the differential equation are singular at a certain value, so sometimes NDSolve crashes ...
5
votes
3answers
184 views

Finding the conditions for degenerate solutions to a cubic equation

I have a cubic equation (corresponding to the band structure of a physical system) given by w in the code below. ...
0
votes
0answers
50 views

How to convert a rational parametric plane curve into implicit form?

This problem is generated from another Green's theorem related question of mine. And here is a forward of the same problem in math.stackexchange. The original equation of the plane curve is not in ...
2
votes
0answers
49 views

ParametricNDSolveValue has a problem with complex numbers

Edited: I have simplified the example compared to before and narrowed the problem down a bit. I would like to use ParametricNDSolveValue as function for data ...
0
votes
2answers
66 views

Create a moving plot along a parametric plot using Manipulate?

I have been looking through Manipulate examples and haven't been able to create a working plot yet. I have a parametric plot defined: ...
0
votes
1answer
79 views

KdV equation - wavebreaking and Galerkin method

I want to show how a wave given by the initial condition: $$ \begin{equation*} \begin{split} u(x, 0) = \left\{\def\arraystretch{1.2}% \begin{array}{@{}c@{\quad}l@{}} 1 - x^2 & \text{for ...
4
votes
1answer
92 views

Substituting ParametricNDSolve for NDSolve

This is my first post so let me know if I need to format things differently. I have been using NDSolve for most problems which optimize parameters for ODEs. I believe that ParametricNDSolve would be ...
0
votes
1answer
80 views

Functions behaving weirdly

The following code f[k_, n_] := Sum[2*(1 + Sum[f[k - j, n - m - j], {j, 1, k - 1}]), {m, 1, n - k + 1}] f[4, 7] f[4, n] gives the output: ...
1
vote
1answer
54 views

Change input parameter order in a function

I'm a beginner in Mathematica programming and I'm trying to understand how input parameters work in Mathematica's function. I encountered a problem with the sequence/order of the input parameters of ...
4
votes
1answer
126 views

Fitting a Parametric Curve

I apologize if this question is obvious or simple. Im in HighSchool and have started playing around with Mathmatica only recently. For my Calculus Final I am suppose to use rotation about the y axis ...
5
votes
1answer
115 views

How to fill the closed region by ParametricPlot with solid color?

I am interested in the following implicit curve with parametric equation: $$ \left\{\quad \begin{array}{rl} x=& 9 \sin 2 t+5 \sin 3 t \\ y=& 9 \cos 2 t-5 \cos 3 t \\ \end{array} \right. $$ ...
2
votes
1answer
47 views

How to plot points using ParametricPlot3D?

I have the following Mathematica code: ParametricPlot3D[{{0 + 0*t, 10 - 1*t, 9 - 1*t}, {7 - t, 7 - t, 6 - t}, {0, 0, -1}}, {t, 12, -20}] The last "parametric ...
1
vote
1answer
44 views

Multiplying two parametric solutions

I'm solving two (1-parameter) differential equations and I want to plot the product of their solutions, how do I do this? Here's the code, ...
3
votes
3answers
295 views

Finding intersections of two parametric curves

I am dealing with the root finding of two parametric data curves (data below). I have already checked Parametric Interpolation of 2D data, which I found useful for plotting, though it is not adequate ...
-2
votes
1answer
63 views

Sign of a symbolic expression as a function of parameter values

I need to know the sign of the following expression for p[t] = z/(1-a), as a function of the parameters {a, b, c, z}: ...
1
vote
2answers
88 views

Plot ParametricNDSolve

I am trying to plot the probability of a molecule being in a certain state via the numerical solution of the Schrödinger's equation of molecule in an oscillating electric field (in a rotating system). ...
0
votes
1answer
136 views

How to convert a system of parametric equations?

I have a system of parametric equations (t is a parameter) ...
0
votes
1answer
78 views

How to plot trajectory for a differential equation in polar coordinates? [duplicate]

I have a differential equation for dr/dt and d[Theta]/dt in terms of r and theta, and I am trying to plot the trajectory in the x-y plane for a given initial condition (r,theta). ...
1
vote
2answers
225 views

How to Fit experimental data with 4D ParametricNDSolve?

Let me first explain the background problem. I'm trying to solve a problem with a projectile motion in 4D such that the position vector is: $\boldsymbol{r}(t)=\boldsymbol{r}[x(t),y(t),z(t)]$ I have ...
7
votes
3answers
207 views

How to combine ParametricPlot and RegionPlot?

I have two implicitly defined equations. I plot the implicit curve using parametric plot. ...
4
votes
1answer
134 views

ParametricPlot3D of Boy's surface

I'm trying to visualize Boy's surface using Bryant's parametrization, as per the MathWorld article. However, I'm not sure I understand the parametrization, and I don't know how to implement it when ...
0
votes
1answer
74 views

Plot curves like equation problems

I'm proving to plot and edit some wolfram alpha laminae, but when I try it, I don't have any result, for example: (from:http://blog.wolframalpha.com/data/uploads/2013/07/Curvespt31.cdf) ...
-2
votes
1answer
55 views

Solve on parametric equation produces inequal results

I have a parametric (parameter t) equation in two dimensions (vectors). s = Solve[pt[t] == qt[t], {a, b}] Both pt and qt are parametric lines using a and b as ...
0
votes
1answer
41 views

Error Exporting STL --insufficient elements to export

I am trying to export the following code as an STL file: ...
0
votes
1answer
56 views

Unable to Solve (for arclength parametrization)

I am having trouble with Mathematica while trying to re-parametrize a curve with respect to its arclength. I need to get the old parameter s written in terms of arclength a so the code is ...
0
votes
0answers
41 views

Formating in Mathematica 10 Find the point of intersection of a plane

Hi all i am new here and i am trying to figure out how to correctly format in Mathematica 10...Finding the point of intersection of a line to a plane. I know how to do it by hand. 1) Find the ...
1
vote
1answer
85 views

Plot a parametric equation in cylindrical coordinates

I'm looking for a way to plot this parametric equation on cylindrical coordinates. r = e^t theta = t+1 z = e^2t Any help would be appreciated
2
votes
2answers
81 views

Why is there always a horizontal tail line on the parametric curve?

I am trying to create a smooth, piecewisely continuous and differentiable curve by using Mathematica's Floor function, which is as in: ...
1
vote
1answer
124 views

Eliminating parameter from parametric equation [closed]

In Mathematica Online I tried: Eliminate[{x == t + t^3, y == t - t^3, z == 1 + t^4}, {t}] ...
0
votes
0answers
67 views

ParametricPlot3D doesn't work with components of a vector input

I can't understand why ParametricPlot3D works, when the input is a vector and does not work, when the input is separated components of the vector (it returns an empty plot). The same happens for ...
0
votes
1answer
50 views

What's wrong with the code?

The following code doesn´t fill the base of the picture. ¿Why? ...
0
votes
2answers
213 views

Not seeing plot of solution returned by NDSolve

I am having trouble with generating a parametric plot with the following code: ...
0
votes
1answer
116 views

Use ParametricNDSolve with Plotting

I am attempting to solve a differential equation of the form $$ \frac{dx}{dt}=ax+by \\ \frac{dy}{dt}=cx $$ with parameters $0<a<1$ and $a,b,c \in \mathbb{R}$. I am able to use NDParametric ...
0
votes
1answer
108 views

Plotting Complex Numbers - Functions of Complex Numbers [duplicate]

So I have to generate a few different plots with z, where z is a complete number... z[x_, y_] := x + y*I F[z_] := (25*Pi*z*I)/(1 + 10*Pi*z*I) First, I need to ...
1
vote
2answers
69 views

Finding roots of a function with a varying parameter

So I'm brand new to Mathematica, and basically what I want to do is find the roots of a function at varying time intervals. The function I'm using is: ...
0
votes
0answers
46 views

System of ODEs with Parameters

FYI: I am new to Mathematica so my questions are probably pretty amateur. I am attempting to write a code to numerically solve the system of equations: {dp/dt= ap-bpx {dx/dt= spx-yx where t is the ...
1
vote
1answer
190 views

Solve a system of parametric equations

I have a system of parametric equations (with a total number of 8). I tried to solve this system by using Solve. I have not received an answer after about 4 hours! ...
-4
votes
1answer
67 views

NDSolve a differential equation depending on some parameter

I have to solve the differential equation, to get a plot of T and R, ...
4
votes
2answers
209 views

How to plot this region?

Consider the $2\times 2$ matrices \begin{align} A=\begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix} \end{align} and \begin{align} B=\begin{bmatrix} b_{11} & b_{12} \\ ...
0
votes
0answers
202 views

Find $\phi$ as function of $\theta$ for Villarceau circle in a torus

May I request for your indulgence, to enable Villarceau circles visualization made by the tip of a line rotating inside a circular torus if possible based on unification of parameters. EDIT2: ...