Maple Questions and Posts

These are Posts and Questions associated with the product, Maple


Hi, I am struggling a bit animating a result that I have.

Let me explain.

I solved numerically some equations for me movement of a rolling disc and a bar bolted to the center of the disc.

So I have a long list of values for:

x[h] for the horizontal position of the disc
beta[h] for the rotation of the disc
theta[h] for the rotation of the bar

and so on...

Then I created a procedure that, for a given instant "h", maple plots the disc and the bar correctly.

Now I want to anumate this procedure that should depend only on the instant h and I cannot perform it.
Maybe the error comes from the fact that there are not functions involved but numerical data, or maybe it is the fact that disc radius and bar lenght are assigned outside the procedure.

Any help would be appreciated.

This is the file:

Mechanics.mw
 

i want to calculate the eigenvalues and  the spectral radius of this matrix can anyone help me 

B:=Matrix([[a, -b, e], [c, l, d], [-e, -k, m]]

When I tried to solve the following integral, Maple returns it unevaluated. What am I doing wrong?

int(ln(a^2+x^2)/(a^2+x^2)^n, x = 0 .. infinity)

I have a system of equations to solve. After that I get a lot of solutions (in attached example it is not such a big number, but I have larger system with hundreds of solutions). After that I have to put all the solutions into function, one by one and calculate it (for each solution). What is the best way to that? For small number of solutions I did it manually.    

Here is this example:

example.mw

 

I am installing maple 2019 on Linux 64 bit. I used the option

--mode text

The installer has not proceeded after answering Y to the following. 

Activate Maple 2019 now (requires an Internet connection). [Y/n]:

Any suggestions? 

Not sure if i'm missing something, but this does not seem to work how i would expect.

Trying to understand why the [1,1] element is simplifed to -3, as well as the [3,3] element to -2. 

Any ideas?

thanks!
 

restart:

MM:=Matrix(convert("{{1/2 (-2 \[Kappa] - 4 \[Lambda]), -2 Sqrt[2] g, 0}, {g/Sqrt[
  2], -\[CapitalGamma] - \[Kappa]/2 - \[Lambda], -Sqrt[2] g}, {0,
  Sqrt[2] g, -2 \[CapitalGamma]}}", FromMma));

"[[[-1/2 2(Kappa)-1/2 4(Lambda),-2 sqrt(2) g,0],[(g)/(sqrt(2)),-CapitalGamma-1/2 Kappa-Lambda,-sqrt(2) g],[0,sqrt(2) g,-2(CapitalGamma)]]]"

(1)

simplify(MM); #why is the first element simplified this way?

Matrix(3, 3, {(1, 1) = -3, (1, 2) = -2*sqrt(2)*g, (1, 3) = 0, (2, 1) = (1/2)*sqrt(2)*g, (2, 2) = -CapitalGamma-(1/2)*Kappa-Lambda, (2, 3) = -sqrt(2)*g, (3, 1) = 0, (3, 2) = sqrt(2)*g, (3, 3) = -2})

(2)

 


 

Download translate_from_mma.mw

I am using Maple 18 to plot iterates of a discrete map.  A vector R1 is parametrized by the label b that runs from 0 - 2*Pi.  The following initial iterate gives me a blue circle:  

>a := 1.0
>q := a*cos(b)
>p := a*sin(b)
>R1 := PositionVector([q, p], cartesian[x, y])
>PlotPositionVector(R1, b = 0 .. 2*Pi);

Is there a way for me to assign a gradient colorscheme to each point of the circle, using b as parameter from 0 - 2*Pi? I have tried using the following, which does not give an error message, but it also just gives me a blue circle:

>PlotPositionVector(R1, b = 0 .. 2*Pi, curveoptions = [colorscheme = ["valuesplit"]]);

I am not sure how to use the vector and mapping options in the command >plotcommand(plotargs, colorscheme=["valuesplit", V, mapping]) to obtain the color gradient along the circle.

Hello, I'm trying to build a function of two variables which has also and index that will be useful later when I will substitue indexed varaibles

f[i] := (x,y) -> a[i]*x + b[i]*y;
f[3](x,y)  -------> expecting: 
a[3]*x + b[3]*y , but it gives f3(x,y)

 

Any suggestion?

 

Dear Support

I am attempting to model quantum dynamics, and have defined a coupled set of nonlinear PDEs I would like to solve for coupled solutions u(x,y,t) and v(x,y,t) using MAPLE 18.

I attach an image of part of the worksheet the pair of PDEs...The initial conditions u(x,y,0), v(x,y,0) are a pair of respectively positive and negative 2D gaussians on the x,y, domain.

Before I go any further, please would you check that MAPLE 18 is in principle capable of finding solutions u(x,y,t), v(x,y,t) solutions, and let me know whether it is worth pursuing the solution?  I have had a look at the MAPLE documentation, but am not sure whether MAPLE can solve this system.

As a warm-up, I successfully solved a 1-D system u(x,t), v(x,t) using pdsolve[numeric], but I am not clear whether MAPLE 18 can solve for u(x,y,t), v(x,y,t) either numerically or analytically on the [x,y,t] domain.

I hope you can provide help/guidance. An image the equations in MAPLE is displayed here...

Melvin Brown

UK

Forgive me for asking but I can't seem to find it in the docs, how do I create a plot which has a categoric variable rather than just real ones? i.e. having it print string labels along one axis rather than integers..

Also hoping this is possible on a 3D graph where each category is associated with 2 real values, i.e. a slice of the 3D plot...

 

Thanks



 Anyone can explain to me this program using Runge Kutta fourth order method

Download program.mwprogram.mw

Anyone can explain to me the Runge Kutta method using the following equations and conditions??

 

diff (diff (diff (f (eta), eta), eta), eta)+ f (eta)* diff (diff (f (eta), eta), eta)=0

diff (diff (theta (eta), eta), eta)+ f (eta)* diff (theta (eta), eta)=0

f(0) = 0, (D(f))(0) = 0, (D(f))(5) = 1

theta(0) = 1, theta(5) = 0

In DifferentialGeometry package, let P be the output of Prolong applied to a Transformation.

How to extract each identity/equation from P?

Is there a way to convert P to an array of equations?

 

In this Post I derive the differential equations of motion of a homogeneous elliptic lamina of mass m and the major and minor axes of lengths of a and b which rolls without slipping along the horizontal x axis within the vertical xy plane.

If the initial angular velocity is large enough, the ellipse will roll forever and go to ±∞ in the x direction, otherwise it will just rock.

I have attached two files:

 rolling-ellipse.mw
        Worksheet to solve the differential equations and animate the motion

rolling-ellipse.pdf
         Documentation containing the derivation of the differential equations

And here are two animations extracted from the worksheet.

I am learning how to use dchange in Maple. I can do  something as dchange(x=t^2) OK, but I need to do dchange(x=t^n) where "n" is meant to be a parameter that I can later use subs on to set it to any number I want.  But I do not know how to tell Maple that "t" is the new variable and that "n" is meant to be used as constant or parameter.

As an example, this works

n:=2;
ode:=x^2*diff(z(x),x)=0;
PDEtools:-dchange({x=t^n},ode,{t})

But this does not work

n:='n';
ode:=x^2*diff(z(x),x)=0;
PDEtools:-dchange({x=t^n},ode,{t});
subs(n=2,%)

It used "n" above as new variable. So the dependent variable which was z(x) became z(t,n). 

So I need to tell Maple that "t" is the new variable only and not "n" as well. 

Is it possible to do this in Maple?

Maple 2019 on windows.

 

Hi,

I compute a double integral, and I would like to change the order of integration ( of course we take into account the domain of integration, that must be changed), but unfortunately I have two different values instead the same value.

order_integration.mw

Note that I the code if I put t_0=0, I get the same value. Bur for other values of t_0, i havent the same value.

Many thanks for your help

 

1 2 3 4 5 6 7 Last Page 2 of 1531