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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2
votes
1answer
46 views

Plotting certain time points in a parametric equation? [on hold]

I'm using Mathematica 5.0 and I have the following problem. I have the following parametric equation that I plotted successfully. ...
0
votes
1answer
56 views

ParametricPlot3D crashes Kernel when called repeatedly in loop

I have a parametric function surf[u,v]. It can be plotted successfully like this: ...
-1
votes
0answers
22 views

How to find the real values of the parameter a, so that the inequation doesn't have positive solutions? [migrated]

The inequation is the following: (x^2 - 6ax + 2x - 5a - 1) / (x+a+1) < 0 If we write this inequation like a/b <0, I may say that for a=0, I found that X1=3a -1-sqrt(9a^2-a+2) X2=3a ...
1
vote
3answers
105 views

Plot multiple functions with different but overlapping intervals

Suppose I numerically solve a differential equation by using sol = ParametricNDSolve[{y'[x] == b y[x], y[0] == 1}, y, {x, 0, 0.3}, {b}] And then I want to plot ...
0
votes
1answer
44 views

Simple grouping equations [closed]

I'm new in the Mathematica world. A very basic question. I have been using the command Eliminate on a set of equations as follow: ...
0
votes
1answer
54 views

Eliminate variable on multiple equations [closed]

I'm pretty new with Mathematica. I have to perform a really simple operation, but I'm really struggling with that. I have a set of 4 equations, for example (they can also be more complex): $ AA = 2 ...
3
votes
1answer
95 views

Plotting a finite series w.r.t. a parameter [closed]

So I would like to plot the series below: $$ S_q = k \frac{1-\sum_{i=1}^{W}(1/W)^q}{1-q} $$ where $k$ is a constant which I assume for now to be equal to 1 and $q \in \mathbb{R}$. However, for my ...
5
votes
1answer
66 views

Continuously varying tube radius

I'm currently trying to draw tubular neighborhoods of torus knots, which Mathematica's "Tube" function allows me to do quite easily. My question regards the appearance of the neighborhood: Is there ...
8
votes
1answer
219 views

How to add a fading trail effect in Animate?

I would like to add a smooth fading effect to the end of a curve, while it is animated. Here's a minimal working example which shows a particle moving on a circle (the circle is drawn while the ...
1
vote
1answer
61 views

Color of lines in ParametricPlot3D

I have a function of two variables which returns a vector of three components. For example func[l_,t_]:={ x=.... y=.... z=.... {x,y,z}} Now I ...
1
vote
1answer
69 views

How to find a maximum value in a rotated parametric plot?

Let me just give you a bunch of tables to reproduce the problem. Here they are ...
5
votes
4answers
138 views

How to correct the name of axis?

In the output of a code I can view that the same axe has two names "z" and "x". How could I correct this? The code is ...
3
votes
2answers
99 views

Plot a parametric function from $\mathbb{R}^2$ to $\mathbb{R}^2$

I want to plot the following function defined on $[-1,1]\times[-1,1]\setminus(0,0)$: $$ F(x,y,t)= \begin{cases} (1-t)(x,y)+t(1,\frac{y}{x})& \text{if}\ -x\leq y\leq x \\ ...
1
vote
1answer
84 views

PametricPlot3D vs ContourPlot3D

Basically, I don't know whether I am missing something mathematically fundamental or I misued Mathematica's functions. ...
0
votes
1answer
75 views

Fourier Series and epicycles - How to find the radii and angular velocities from a function's Fourier Series expansion

The following code is a bit clumsy, but it constructs a variable number (n) of epicycles using the values from the radii and angularVel tables that follows the path of a parametric given as a sum of ...
3
votes
2answers
80 views

Defining special function or variable for a derivative in mathematica

I have a question in Mathematica, I would appreciate it if you possibly answered me. What can I do for defining a special variable for derivative of arbitrary variable. For example, imagine I have a ...
7
votes
2answers
155 views

Parametric plot on multi-dimensional domain

I wish to plot all the points in 3 space that satisfy the following conditions. $$ (x,y,z) = (a^2+b^2, ac+bd, c^2+d^2) $$ for $a,b,c,d$ in some range. I have tried the following. ...
1
vote
0answers
45 views

Fitting data using ParametricNDSolveValue and NonlinearModelFit [closed]

I'm trying to evaluate the kinetics of the chemical reaction. For that I need to fit my experimental data to the kinetic equation. These are my steps in Mathematica. ...
5
votes
0answers
91 views

Find regions in which the roots of a third degree polynomial are real

I have to find the roots of a third degree polynomial in $\phi$ that depends from 3 parameters, namely $t,s,w\in \mathbb R$. In order to do that I've used the command ...
3
votes
3answers
111 views

Filling between multivalued curve and normal curve

I have a multivalued curve p1 (left curve) and a normal curve xpr2 (right), and I want to fill the middle region between them as blue, and the rightmost region as red. However, I get this extra ...
1
vote
2answers
74 views

Creating B-splines using a For Loop

I'm very new to Mathematica (as will make itself clear with this question) and I'm trying to create a program that makes b-splines to fit n points. I'm not quite sure how to reference the i-th point ...
1
vote
1answer
72 views

Solving PDE for a parametric function, using ParametricNDSolve

I've to solve a $4 \times 4$ matrix PDE which involves the following matrices: ...
3
votes
2answers
335 views

Solve stiff system by shooting method

I'm trying to solve a second order differential equation with the shooting method but, it appears to be a stiff system. This is worst for a larger parameter $\mu$. I've tried different methods: ...
1
vote
2answers
72 views

Need help getting the intercept of two lines in a ContourPlot

I am trying to find a set of parameters $\{\epsilon,\epsilon_b\}$, so that the two local minima have exactly the difference of 15.1 (see code below) and the left sided local minimum and the local ...
3
votes
0answers
71 views

Schwarz-Christoffel toolbox

Is there a toolbox for working with Schwarz-Christoffel transformations in Mathematica? More generally, is there a toolbox for visualizing conformal mappings in the complex plane? There are a lot of ...
2
votes
1answer
217 views

Plot a function for different parameters

Suppose I have a function that I want to plot for several values of a parameter all in the same window. For instance the function $f$ defined as ...
1
vote
1answer
66 views

Trajectories of system of parametric equations

I have to obtain plots of trajectories for (theta(t),u(t)) and then overlay them with a contour plot. The overlaying with the contour plot it is easy. What trubles me though is the trajectory part. ...
4
votes
1answer
97 views

Inverse of parametrized ellipse area

If you parametrize an ellipse (with the center, not a focus, at the origin) as: {a Cos[t], b Sin[t]} the area traced out from the focus (not origin) for a given ...
2
votes
3answers
165 views

Parametric Plot on Surface of Sphere

I have a set of parametric equations in spherical coordinates that supposedly form circle trajectories. See below: ...
0
votes
1answer
63 views

How to plot a linear vector tangent to a bezier surface?

I have a bezier surface and its parameters are u and v. The partial differentiation with u as variable gives me a vector in the direction of u. I need to plot this vector. I plugged in a particular ...
1
vote
3answers
186 views

Fit dataset with customized discontinuous distribution

I have the following parametric CDF: F[x_, λ_, β_, γ_] = Piecewise[{ {0, x < 0}, {1 - (1 - β) E^(-x λ), 0 <= x < γ }, {1, x >= γ} }]; ...
1
vote
1answer
68 views

Differentiate functions

I have two functions: F1[t_, g_] := a1*t + a2*g F2[t_, g_] := b1*t + b2*g I want to evaluate $(dt/dF1)_{F2}$; i.e., differentiate $t$ over $F1$ when $F2$ is ...
0
votes
2answers
157 views

Parametric Region Plot

I tried to find solution in a few discussions but I couldn't solve my problem because my knowledge is basic. I have the following functions and parameters: ...
7
votes
4answers
472 views

How do you find the self-intersection points of a single parametric trigonometric function? [duplicate]

How do you use Solve or FindRoot or other Mathematica functions to find the points at which the graph of ${\bf a}(t) = 3 \cos ...
2
votes
2answers
184 views

How do I rotate a curve?

I have a circular segment defined as: ParametricPlot[5 {Sin[ϕ], 1 - Cos[ϕ]}, {ϕ, -0.2, 0.8}, PlotRange -> All] which I have to rotate around point ...
0
votes
1answer
100 views

How to plot the position vector r(t) = 3 cos(3.3πt)i + (sin(4πt) + 4t)j with t being a min of 0 and max of 1? [closed]

Every time I try using the ParametricPlot, nothing shows up. This is what i've done so far: ParametricPlot[{[3 cos[3.3 πt]], [sin[4 πt] + 4 t]}, {t, 0, 1},
0
votes
1answer
119 views

Solve a function to find the optimum value of parameter in mathematica [duplicate]

I have a complicated function as shown It doesn't have a standard integration as far as I know. Now, numerical integration of the left hand side function over a set of points gives the right hand ...
0
votes
0answers
39 views

How do I change a 3d bspline curve to a polygon based graphic? [duplicate]

I have a graphics image generated with bsplines: Graphics3D[Tube[BSplineCurve[pts], 2]] I want to export this to a .stl file. To do so I know I need to modify ...
8
votes
1answer
169 views

Is it possible to speed up the user-defined function CAGDBezierSurface?

For given control net of points $P_{i,j} \quad i=0,2, \cdots m, \quad j=0,2,\cdots, n$, the Bézier surface is defined by the following equation: ...
10
votes
2answers
371 views

A problem about the implementation of Bezier curve

I implemented the Bezier curve like built-in BezierCurve as follow: SplineDegree -> d specifies that the underlying ...
3
votes
1answer
162 views

How to change parameters to equations of physical properties they belong to in an equation?

First off, I want to apologize for my poor English as I am not a native speaker. In my physics research, I had to solve a system of equations, from which I would get a solution for the speed of an ...
-2
votes
1answer
72 views

Plot the result of NIntegrate for different parameter values

I want to plot the result of a numerical integration containing a parameter in terms of the parameter. The code is: ...
0
votes
0answers
57 views

How to solve algebra equations containing integration and parameters?

I'm trying to solve two nonlinear algebra equations for two unknown parameters, U and Tf. Since some terms in these equations contain integration, and the integration also contains U and Tf. The main ...
1
vote
2answers
255 views

Plotting a parametric function containing an integral [closed]

I need to plot this expression $$ \phi(s; H,B)=\left(\int_{0}^{s}\frac{1+B\ \sin2H\ t}{\sqrt{1+B^2+2B\sin2H\ t}} \text{d} t,\ \frac{1}{2H}\sqrt{1+B^2+2B\sin2H\ s}\right)$$ for $H=0.5$, $B=0, 0.5, 1, ...
1
vote
1answer
88 views

Adding a fading color only to 3D curves going outside a cylinder

I'm having a problem with color shades on multi curves drawn with the Mathematica 7.0 code below. All the curves with both their endpoints inside the unit cylinder (green circle on the picture below) ...
1
vote
1answer
94 views

Adding a fading color to multiple lines in 3D

I would like to add a fading color to all the 3D lines I'm drawing with the code below, but I'm having difficulties with implementing the idea. The curves are starting on a unit sphere, and extend in ...
6
votes
1answer
369 views

Dipolar magnetic field lines inside a cylinder

I'm drawing the magnetic field lines of a rotating dipole (magnetic field distorded by emission of radiation). Currently, my Mathematica 7.0 code is fully working, but I'm having a constraint which I ...
0
votes
1answer
86 views

Colors on a 3D curve not working

I'm having troubles applying colors to a simple 3D curve plot. Here's the code : ...
14
votes
2answers
427 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
181 views

How to obtain the area enclosed by such a curve?

The desired curve is defined as curve02 below : ...