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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1answer
68 views

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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0answers
54 views

Vector Parametric Plot different from polar plot using norm of vector

I've defined two vector functions (2D) of real variables and then I plotted them parametrically using ParametricPlot[]. The result is the green and orange curves (the blue curve is a reference circle)....
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0answers
72 views

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 ...
1
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1answer
43 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, ...
3
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1answer
56 views

How to calculate the derivative of the solution of ParametricNDSolveValue?

Consider the following code: ...
0
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1answer
75 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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0answers
31 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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0answers
51 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 ...
0
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1answer
64 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 ...
3
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2answers
134 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
70 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
65 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 $...
0
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1answer
64 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]}]. ...
2
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1answer
107 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. ...
1
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2answers
51 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 <...
4
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3answers
180 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 ...
4
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2answers
152 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'...
2
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1answer
84 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 ...
2
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2answers
79 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 ...
1
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1answer
48 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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0answers
58 views

Spheroidal Harmonics

There is a (scalar) field P varying on a spheroid (squashed) surface. This field is a function of four independent components ...
3
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1answer
86 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
54 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, ...
1
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1answer
79 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 '...
1
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1answer
71 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
95 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 ...
0
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1answer
76 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 ...
0
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1answer
48 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 ...
1
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1answer
55 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. ...
0
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1answer
54 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
69 views

3D Arrow path along a surface

I have the following two surfaces, created by the following functions ...
3
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1answer
52 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 <...
1
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1answer
94 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 ...
1
vote
1answer
71 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: ...
1
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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 ...
0
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1answer
44 views

Remove specific terms from Mathematica output

I have a very complicated output from Mathematica - which may run to several pages - and I want to keep only some of the terms. The expression I am working with is a double summation. It results in (...
0
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1answer
33 views

How to find the expected value of a parametric function?

Suppose $a \ge 0$ is a parameter and $X_1$ is an uniform random variable in $[1,4]$ and $X_2$ is an uniform random variable in $[1/2,1]$. How to find the expected value of $\max\{5-X_1a, 3-X_2a,0\}$?
2
votes
2answers
134 views

Minimization using NMinimize

I have a system of ODEs say $$x'(t)=2 x(t)-x(t)y(t)-3 x(t) g(t),$$ $$y'(t)= y(t)-2 x(t)y(t)- x(t) g(t)$$ with ICs $x(0)= 1, y(0)=1/2$, say, for $t_0 \leqslant t \leqslant t_f$, where $t_0$ and $t_f$ ...
5
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2answers
140 views

Plot f(x),f(y),alpha where f(x) and f(y) are the solutions of a two ODEs system depending on a parameter α [closed]

My question is in the title. For example, the system could be: $$\begin{align*}\frac{dx}{dt}&=-y+x[\alpha-(x^2+y^2)]\\\frac{dy}{dt}&=x+y[\alpha-(x^2+y^2)]\end{align*}$$ And I want to plot this ...
0
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2answers
62 views

Unexpected results when plotting an output of Solve [closed]

My aim I want to find the solution of a cubic equation as a function of a parameter. In my code, the cubic equation is to be solved for the variable th with ...
2
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0answers
90 views

Repeated calling of a ParametricNDSolve result in a faster way?

I recently learned of ParametricNDSolve and found that I need to compute it once and then call its result sol at different ...
1
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2answers
71 views

Colour each graph differently

I have a Manipulate function, which allows me to compile plots on a single plot (see below). I am trying to make each line on the compiled plot to be a different ...
0
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1answer
31 views

Parametric Maximization of a function with indicator function

How is it possible to determine the maximum and maximizer of the following function? where I(x>0) = 1 if x>0, otherwise 0 ...
0
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2answers
67 views

Add function to Manipulate

I have a Manipulate plot and want to add another function, in addition to the existing a and ...
1
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1answer
51 views

ParametricNDSolve Value and Manipulate with 3 parameters

I am trying to solve a set of coupled differential equations, using ParametricNDSolveValue, where there are 3 parameters. The parameters are ...
0
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0answers
38 views

Fit data to a model of two-variable differential equations

I am trying to fit some data to the solution of a differential equation. I am using ParametricNDSolve to create a model which should fit the data using ...

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