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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43 views

Defining parametric function resulting from DSolve

I am trying to define a function that is a solution of a simple ODE with a parameter, for example ...
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1answer
63 views

How to get a specific component of an equation without hardcoding? [closed]

Say I define an equation line[t_] = {t, 2t, 3t}. What code will define x[t] = t, y[t] = 2t, ...
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1answer
69 views

How to make Sphere Transparent using ParametricPlot3D

This is the code I used Edit: This is the full code to create this image ...
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1answer
49 views
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2answers
325 views

Olympic Athletics Track

Writing: ...
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2answers
108 views

Unpacking a Mathematica expression returned by DSolve

I was trying to solve a system of differential equations in Mathematica and had troubles understanding what the solution looked like. So I wanted help to unpack it. I had a system of two coupled ...
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77 views

Singularity or stiff system in ParametricNDSolve

I have following parameters and equations(it's a complex one, please check it :) ): ...
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1answer
76 views

Does mathematica cache the interpolating function from ParametricNDSolve?

I want to evaluate the solution of a system of non-linear ODEs using ParametricNDSolve. The output of ParametricNDSolve is a ParametricFunction object. Let's call it $f_\theta(t)$, where $\theta$ is a ...
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1answer
72 views

Shading a surface bound by a curve in 3D

Foundation Input: unit circle The exercise deals with transformations of the unit circle, $(\cos \theta, \sin \theta)$. We start with the unit circle with Hue coloring over the angular range of $(-\pi,...
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1answer
42 views

How to use ParametricPlot3D with ParametricFunction objects? [duplicate]

My code produces the iconic figure showing the error threshold of the quasispecies model. ...
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2answers
142 views

Use solutions of FindRoot in subsequent calculations

I want to solve the equation $b e^a = 2$ in $b$, for values of $a$ ranging from $0$ to $10$ and each time $a$ to be increased by $0.1$. So I have: ...
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1answer
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Solution for inequality equation - "Cannot be solved with the methods available to Reduce"

I am trying to solve the following inequality for $v$: $b>e^{\frac{-v}{\alpha}}\cdot \alpha + v$. (Where I know: $b>0$, $v \in [0, 1]$, and $\alpha >0$). However the following doesn't work: <...
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Solving 2nd order coupled differential equations using shooting method

I'm trying to solve these two coupled 2nd order differential equations: with the following boundary conditions: where $r_{*}$ is the value of the $r$ at midpoint. I was trying to solve these ...
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1answer
44 views

How to pass results of computations to a function definition?

Here is the following code that works, F[{x_,y_,z_}]:={16(y-x), x(45-z)-y, x*y-4z); x = Array[a,3]; F[x] and the answer is, ...
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1answer
59 views

How to calculate the derivative of the solution of ParametricNDSolveValue?

Consider the following code: ...
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1answer
84 views

How to derive all KKT points of a parametric optimization problem

Suppose we have a symbolic optimization problem where all parameters and decision variables are nonnegative like the following problem. I would be thankful to know if there is any method to find all (...
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33 views

Issue with Piecewise Parametric Plotting

I am trying to make a parametric plot of a piecewise function that is defined locally. For some odd reason, Mathematica will only plot the first two pieces of the piecewise function. If I plug in ...
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55 views

Solving a matrix differential equation by using a function that takes a matrix as its argument

I have a function g of the form g[y_]:=A.y.B where y is a 2-by-2 matrix whose elements are ...
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1answer
72 views

When should one use RegionFunction with ParametricPlot3D?

According to the documentation, "RegionFunction is an option for plotting functions that specifies the region to include in the plot drawn", and it can be ...
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2answers
148 views

Find intersection points between ParametricRegion and other curves

How do you instruct Mathematica to return intersection points between curves as numerical values, when using ParametricRegion to represent at least one of the ...
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0answers
72 views

Plotting two functions values in two axis

I have two multivariate functions $f_1(x,y)$ and $f_2(x,y)$. I want a plot in which in the horizontal axis I have the values of $f_1$ in a specific point $(a,b)$ and on the vertical axis I have the ...
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1answer
43 views

Plotting a set of parametric equations using only points

I am using ParametricPlot3D to plot a superellipsoid using the code below: ...
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2answers
75 views

How to illustrate schematically (animated) solutions of a system of $3$-variable equations by increasing one of the variables with step $0.01$?

Following my previous question here, I am looking an alternative way to solve this problem (the method was not applicable to more complicated situations). I have a system of two 3-variable equations $...
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1answer
67 views

ParametricPlot3D with variable plot limits

I would like to use ParametricPlot3D in the following general way: ParametricPlot3D[\[Sigma][u,v],{u,0,2Pi},{v,-f[u],f[u]}]. ...
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1answer
118 views

How can I combine two parametric plots in a continuous one?

I'm studying the Ekman spiral for piecewise uniform viscosity. So I have two velocity components (u,v) for every layer. One pair for the sufrace and one pair for the layer below. ...
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2answers
52 views

Error when integrating with constants?

I'm trying to integrate an ellipse: (x^2)/alpha^2) + ((y^2)/beta^2) = 1. I am not sure if I should have insert constants for alpha and beta or if there's a way to keep them there. This is my code <...
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3answers
183 views

How to find absolute minimum with NMinimize

So I have a trefoil and twisted cubic that are very close to intersecting but do not. I know NMinimize can be used to best approximate the minimum, but it ...
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2answers
156 views

Plotting a parametric function on xy, xz, and yz planes

I'm trying to plot a trefoil with a parametric function in Mathematica. How would I do that? I know I can use Parametric3D to depict all of it but how do I project it on the XY, XZ, and YZ planes? It'...
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1answer
92 views

Plotting equation of motion in mathematica [closed]

Suppose I have an equation of a moving body in Newtonian Mechanics e.g. $ax^2=(b/t^4)+(c/t^2)$ how can I plot a x-t graph in mathematica with a range for the constants a, b and c from 0 to 5 with ...
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2answers
85 views

Animating a Parametric Plot of Planetary Motion

I have been trying to make a simple animation of planetary motion, but I can't seem to get it to work. I'm still new to this program so I am not sure how to make it work. Can anyone help? Here is my ...
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1answer
49 views

How to initiate a matrix with indexed parameters [closed]

I couldn't find it in the documentation, so I'm posting it here. I want to create two by two matrices as follows: $$ `W = \begin{bmatrix}w_{11} & w_{12} \\ w_{21} & w_{22} \end{bmatrix}, V = \...
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60 views

Spheroidal Harmonics

There is a (scalar) field P varying on a spheroid (squashed) surface. This field is a function of four independent components ...
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1answer
87 views

How to Create Lissajous Figures for Driven Damped Pendulum (as an animation/with Manipulate)

I wanted to know how can I generate a Lissajous plot for the forced driven pendulums (but for one pendulum in my case): (https://demonstrations.wolfram.com/ForcedPendulumsWithDamping/). I tried using ...
2
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1answer
61 views

Converting a Non-Simple Closed Curve in an Image to a Parametric Equation

I would like to generate a parametric equation for a non-simple closed curve defined in a 2D image (shown below). This is the same problem as described in this question for simple curves. However, ...
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1answer
80 views

Avoiding/skipping singularity error in ParametricNDSolve

I've looked up a few examples of similar errors for ODE's with singular points, but have yet to figure out a way to solve this problem for my case. A simple patch up where the singular point is '...
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1answer
78 views

How to solve integro-differential with parameters iteratively?

I am trying to solve an integro-differential equation and tried using one of the answers that I found in a related question: Numerically solve an integro-differential equation The difference is I have ...
2
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1answer
99 views

Plotting multiple dependent variables with DSolve (projectile motion with air resistance)

I wrote a working code that plots what I need using DSolve and parametric plot. Here's an example of what it plots (and code is at the bottom). However, I want to be able to plot multiple graphs on ...
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1answer
93 views

How to solve this set of PDE equations? I tried ParametricNDSolve, but

I am tring to solve set of PDE equations with parameters of v[z],q[z],T[z,t,r]. Below is my ...
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1answer
50 views

Issue with ParametricNDSolve and Table

I have a differential equation, I plot it for different initial values by using ParametricNDSOlve. Code - ...
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0answers
40 views

NSolve with ParametricFunction

I have solved a SDE with ParametricNDSolve: s = ParametricNDSolve[ {p1, m1, p0, m0}, {P, m}, {r, 0, 1}, {m, k, e, Cnew} ] And now I want to treat the ...
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1answer
57 views

Plot with three functions and three parameters [closed]

I think my code doesn't have any problem but the program shows me this error and I'm confused! Plot::argr: Plot called with 1 argument; 2 arguments are expected. ...
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1answer
57 views

How can I substitute values into this set of equations?

I'm new to Mathematica and I'm trying to solve this set of trig equations (I'm not exactly sure if the syntax looks correct): ...
2
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1answer
71 views

3D Arrow path along a surface

I have the following two surfaces, created by the following functions ...
3
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1answer
54 views

Marking with Mesh, Distinct coloring, Ticksing, and Plotting table of complex function with parametric plot

Here is my todo list and what i've done: Using FrameTicks on specific points only (failed). Plotting six graphs with Table on <...
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1answer
97 views

Solving multiple differential equations parametrically

I have the following code, where I am trying to solve one set of differential equations parametrically. I then want to use this solution to solve another equation parametrically. However, I get the ...
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1answer
76 views

How to get the intersection between circle and rectangle?

Consider two figures: a rectangle with coordinates $(x_{min},y_{min}), (x_{min}+dx,y_{min}+dy)$, and a circle. The latter has a radius $R$ and is located at the center of the coordinate frame. How to ...
2
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1answer
31 views

Gaps in a continuous parametric plot problem

I attempted to plot a parametric plot using the following code: ...
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2answers
53 views

Solving a hyperbolic equation

I have the following equation: Tanh[-19.4*\[Zeta]]*Exp[k x] == Tanh[-19.4*\[Psi]]; \[Zeta] = 66; k x = 9.21; I want to calculate the value of ...

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