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Does this condition happen when the character is too long?

Hello everybody,

i am trying to use PDEchangecoords to transform a system of differential equations from Cartesian coordinates to toroidal coordinates. However, when i use a user defined coordinate transform from toroidal to Cartesian, i don't get the initial equations. Please find attached a minimal working environment.

i would highly appreciate your hints and suggestions!

Thank you

Best regards,

F

question.mw
 

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NULL

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restart; with(DEtools); addcoords(invToroidal, [xi, eta, phi], [sinh(xi)*cos(phi)/(cosh(xi)-cos(eta)), sinh(xi)*sin(phi)/(cosh(xi)-cos(eta)), sin(eta)/(cosh(xi)-cos(eta))]); PDEchangecoords(diff(f(x, y, z), z), [x, y, z], toroidal, [xi, eta, phi]); PDEchangecoords(%, [xi, eta, phi], invToroidal, [x, y, z]); print("i would expect here to get", diff(f(x, y, z), z))

"i would expect here to get", diff(f(x, y, z), z)

(1)

NULL


 

Download question.mw

 

Hello Everyone!

I have one more challenge for you.

How can I find for a Free-Pinned-Pinned-Free (3-span) beam (Picture A below) using the Krylov–Duncan Method (Literature links and references below):

- the matrix of the system?

- the transcendental equation in order to determine the natural frequencies?

- the first three mode shapes?

I tried to do it as you can see from my MAPLE (file below), but I got stuck when I use the command "determinant" and it did not find the transcendental equation.

Krylov_function_free_pinned_pinned_free_beam.mw

 

Picture_A

References:

Krylov–Duncan Method
https://link.springer.com/content/pdf/10.1007%2F978-1-4419-1047-9_14.pdf
 

Krylov–Duncan Functions - page 96

You can find that book using the https://libgen.is/
https://www.amazon.com/Formulas-Structural-Dynamics-Tables-Solutions/dp/0071367128

Hello.

I would like to solve numerically highly nonlinear and cumbersome the second order differential equation. 

Applying the numerical procedure I got an error "Error, (in dsolve) found wrong extra argument(s): range = 0 .. 4*Pi, type = numerical". The similar problem has been described earlier here however I can't realize my problem. 

Below is my code

restart;

A1 := 8*Pi^3*R^2*n(x)^4*m+(2*Pi*sin((1/2)*x)*m*omega0*p+Pi*sin((1/2)*x)*m*omega0+3*Pi^2*(diff(n(x), x, x)))*n(x)^3+(-2*sin((1/2)*x)^2*m^2*omega0^2*p^2+2*cos((1/2)*x)^2*m^2*omega0^2*p^2-2*sin((1/2)*x)^2*m^2*omega0^2*p+2*cos((1/2)*x)^2*m^2*omega0^2*p)*n(x)^2+(-4*(diff(n(x), x, x))*sin((1/2)*x)^2*m^2*omega0^2*p^2-8*sin((1/2)*x)*(diff(n(x), x))*cos((1/2)*x)*m^2*omega0^2*p^2-4*(diff(n(x), x, x))*sin((1/2)*x)^2*m^2*omega0^2*p-8*sin((1/2)*x)*(diff(n(x), x))*cos((1/2)*x)*m^2*omega0^2*p)*n(x)+8*sin((1/2)*x)^2*(diff(n(x), x))^2*m^2*omega0^2*p^2+8*sin((1/2)*x)^2*(diff(n(x), x))^2*m^2*omega0^2*p;

R := 1; m := 1; p := 10; omega0 := 1000;

A2 := A1;

with(plots):
A3 := dsolve({A2, n(0) = n(4*Pi), (D(n))(0) = (D(n))(4*Pi)}, type = numerical, range = 0 .. 4*Pi):

odeplot(A3);


I appreciate for any help and suggestion.

 

Help required to plot the real part only in  multiple plots. i have written some codes  please help me to rectify the errors.Thanks in advance

 

restart:
with(plots):
n:=0.75:Eh:=100:mn:=1:t0:=0.2:
a1:=(mn/t0)^((n-1)/(n))*(tb)^(1/n):a3:=Eh/tb:a4:=(Eh)^2:
U1:=(a1/Eh)*(-1+(a3*r/Eh))^(1/n)*(n*a4/(1+n))*(1/a3-(r/Eh))-a1*(-1+(1/tb))^(1/n)*(n/(n+1)*(tb-1)):
plot([Re(seq(eval(U1,tb=j),j in[0.8,0.9,1.0]))],r=0..1,legend = [tb =0.8, tb=0.9,tb =1.0],  labels = ["z ", "U"], labeldirections = ["horizontal", "vertical"],  linestyle = [solid,dash,dot],color = [black, red,green]);

I want to shade the area where the two polar curves overlap. The first curve is r=2 and the other curve is r=2(1-cos(theta)). How do I do this?

I want to find the surface area of this parametric curve revolving around the x-axis. I was able to plot the 2D rendering but I want to show the plot so that I can see the surface area. I suspect that would be the 3D rendering.

x=cos(t), y=2+sin(t), 0<=t<=2pi, x-axis

I see this error once in a while

Error, (in SolveTools:-CancelInverses) assertion failed, simplify should not leak _Z variables out from RootOfs 

When I run a long script. Unfortunately, I have not been able to make a small example to reproduce it. So it is random. I've seen it about 5-6 times in the last 2-3 weeks, over 100 runs during this time.

Just wanted to see if anyone saw this before. The strange thing it is random. I can re-run the same script, or restart it from the point where it failed,  with no changes anywhere, and this error do not show up again for days, and suddenly it shows up again.

Must be related how to Maple internal cache memory happened to be arranged at that time. I noticed that a number of things in Maple seem to happen at random times, such as a random hang of the server at different times and places. I could never understand why this happens in Maple.

If there is only one thing Maplesoft could do for the next version, it will be to improve the robustness of its software.

Any chance to get a dataplot with units in one or both axis?

Or is this another thing where units are cause of trouble?

plotunits1.mw

Hi Everyone!

I would like your help again.

Considering a Free-Pinned-Pinned-Free beam (page 88 in the pdf file). In case of a matrix 12x12 how could I find the coefficients (a1, a2, a3, a4, b1, b2, b3, b4, c1, c2, c3, c4) using MAPLE in order to plot the mode shapes of the Figure 3.22 (a) (page 70 in the pdf file)? in case of a matrix 16x16 and  20x20, the procedure is the same?

I tried to plot the mode shapes but I failed because I believe they should be similar to Figure 3.22 (a) (page 70 in the pdf file)

 

sys_GE := {-a1 + a3 = 0, -a2 + a4 = 0, 0.9341161484*a1 + 0.3569692163*a2 + 1.519943120*a3 + 1.819402948*a4 = 0, 0.6669014188*b1 - 0.7451459573*b2 + 5.530777989*b3 + 5.620454178*b4 = 0, 0.9938777922*c1 - 0.1104849953*c2 + 62.17096851*c3 + 62.17901032*c4 = 0, -0.9341161484*a1 - 0.3569692163*a2 + 1.519943120*a3 + 1.819402948*a4 + 0.9341161484*b1 + 0.3569692163*b2 - 1.519943120*b3 - 1.819402948*b4 = 0, -0.3569692163*a1 + 0.9341161484*a2 + 1.819402948*a3 + 1.519943120*a4 + 0.3569692163*b1 - 0.9341161484*b2 - 1.819402948*b3 - 1.519943120*b4 = 0, 0.3569692163*a1 - 0.9341161484*a2 + 1.819402948*a3 + 1.519943120*a4 - 0.3569692163*b1 + 0.9341161484*b2 - 1.819402948*b3 - 1.519943120*b4 = 0, -0.7451459573*b1 - 0.6669014188*b2 + 5.620454178*b3 + 5.530777989*b4 + 0.7451459573*c1 + 0.6669014188*c2 - 5.620454178*c3 - 5.530777989*c4 = 0, -0.6669014188*b1 + 0.7451459573*b2 + 5.530777989*b3 + 5.620454178*b4 + 0.6669014188*c1 - 0.7451459573*c2 - 5.530777989*c3 - 5.620454178*c4 = 0, 0.7451459573*b1 + 0.6669014188*b2 + 5.620454178*b3 + 5.530777989*b4 - 0.7451459573*c1 - 0.6669014188*c2 - 5.620454178*c3 - 5.530777989*c4 = 0}

 

solve(sys_GE, {a1, a2, a3, a4, b1, b2, b3, b4, c1, c2, c3, c4});
        {a1 = 0.1014436637 c4, a2 = -0.1143870369 c4, 

          a3 = 0.1014436637 c4, a4 = -0.1143870369 c4, 

          b1 = 0.07095134140 c4, b2 = -0.1260395712 c4, 

          b3 = 0.1510591164 c4, b4 = -0.1737777468 c4, 

          c1 = 0.2102272829 c4, c2 = -0.2816561313 c4, 

          c3 = -1.003990622 c4, c4 = c4}

26_06_2020_Transcedental_equation_matrix_12x12_artigo_2.mw

Hello everyone, can anyone help me to solve this problem? noted I want to solve a couple of odes and need to find involved integration constant i.e c1 to c4. 
 

restart

diff(q(y), y, y)-A*q(y) = B*(P*y+c1)

diff(diff(q(y), y), y)-A*q(y) = B*(P*y+c1)

(1)

NULL

bc := q(-sigma) = 0, q(sigma) = 0

q(-sigma) = 0, q(sigma) = 0

(2)

(1+N)*(diff(u(y), y, y))+N*(diff(q(y), y)) = P

(1+N)*(diff(diff(u(y), y), y))+N*(diff(q(y), y)) = P

(3)

bc := u(-sigma) = 1, u(sigma) = -k

u(-sigma) = 1, u(sigma) = -k

(4)

``


 

Download help_couple_ode.mw

Hello

I want to know if there is any option to convert the Maple code into MATLAB version to work across platforms. I have tried the code generation option in Maple and I could not understand how to use the single line code generated. I am working on an already written Maple code and conversion of code to use on both platforms is kind of important. Please advice me on the same.

Regards!

I have a string which includes characters from the extended ASCII character set. I simply want to print the string. Nothing fancy. Hence my question is: how does one print characters from the extended ASCII character set so that they show up as the characters and not a bunch of empty boxes?  (A technique for UTF-8  character printing would be a bonus.)   

<Edit> For example, in integers, my string could be:

s := [56, 72, 157, 38];

Hence there printing of s as a string should be a 4 character / bytes entity: 

printf("%s", convert(s, bytes));

 

I work with polarization in optical fibers.  I want to (theoretically) scramble the polarization and cover the entire Poincare sphere with several thousand points using a sequence of two variable retarders.   So looking at the Mueller matrices in the attached image, as I vary the arguments of the sin & cosines, I’d like to see the polarization states traced out on the Poincare sphere.    Has this already been done in Maple, as in some kind of canned routine or add-on module?

Thanks!

Hi, 

While "numpoints=..." is said to be an admissible option of SurfaceOfRevolution (or VolumeOfRevolution, default value set to 50), the graphical results doesn't account for the value of numpoints.

Is this a known issue?

TIA

Surface0fRevolution.mw



 

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