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Hi, I have a procedure named f1. In it, it calls another procedure f couple of times. procedure f does not have recursive calls implemented.

I have no idea what caused the error. Could anyone give a hint?

Thanks a million in advance,

Best,

Jie

I like Maple the most for calculation of difficult parts. But when it comes to display, I am ignorant and do not know how to command the maple for showing me what is visible in the document.

I attach herewith my document which shows in print view only top half of the sketch. What should I do to show all three figures in the portrait page.
(Here below, after uploading it is shown alright, but in the print preview it is not showing!!).

I want to convert the doc to pdf. Therefore, in the doc preview itself it should be complete.

Thanks for help.

Ramakrishnan V
 

NULL

 

NULL

 

 

 

NULL

 

 

``

NULL


 

Download sketchesNotComing_in_full.mw

Hello,

do not work well and U functions are not replaced with series form.

Please see equation 5.

Also, How me can differential with respect to the constant Amnr], Bmnr], Cmnr] as shown in   attached figure?

For Differentiation I need a

Diff.pdf

Hello! I have a Maple sheet that is functional in some versions of Maple but not others. It works perfectly in Maple 18 (which is the version with which it was written), but when running it in Maple 2019, I see the following error:

  • "Error, (in Matrix) cannot determine if this expression is true or false: Distance(Vector[row](3, {(1) = 0., (2) = 1.313799622, (3) = 0}), Vector[row](3, {(1) = 0., (2) = -1.313799622, (3) = 0})) < 99999999999999999999/100000000000000000000"

And believe that it is related to the following lines of code:

  • R := Matrix(N, (i, j) -> Distance(coords[i], coords[j]) ;
  • S := Matrix(N, (i, j) -> if i = j then 1 elif R[i, j] < 3 then (1+C*R[i, j]+(2/5)*C^2*R[i, j]^2+(1/15)*C^3*R[i, j]^3)*exp(-C*R[i, j]) else 0 end if)

It seems as if it cannot compute a distance between two points (as given in the form of two vectors). I have imported the Student:-Precalculus package, along with ArrayTools and LinearAlgebra, at the start of the sheet, but am wondering if there is an issue with this package in other versions of Maple. The full sheet can be provided if more information is needed, but I'm pretty sure that portion is the problem. Any help would be greatly appreciated.

 

Sheet: testsheet.mw

I can use ApproximateInt for the integral?

approximate_int
 

restart

``

 

"f[1,1](r,theta):=(sin(-4.700000000 10^(-6)+4.700000000 r)-0.1369508410 sinh(-4.700000000 10^(-6)+4.700000000 r)) cos(6 theta):"

"L[1, 1](r, theta):=-2* (((&PartialD;)^2)/(&PartialD;r^2) f[1,1](r,theta))+7* f[1,1](r,theta)+5 *f[1,1](r,theta)-(2 *6 (((&PartialD;)^2)/(&PartialD;theta^2) f[1,1](r,theta)))/r+(0.6 (((&PartialD;)^4)/(&PartialD;r^2&PartialD;theta^2) f[1,1](r,theta)))/4+(.5 (((&PartialD;)^4)/(&PartialD;theta^4) f[1,1](r,theta)))/4"

proc (r, theta) options operator, arrow, function_assign; -2*(diff(f[1, 1](r, theta), r, r))+12*f[1, 1](r, theta)-12*(diff(f[1, 1](r, theta), theta, theta))/r+.6*(diff(f[1, 1](r, theta), r, r, theta, theta))/4+.5*(diff(f[1, 1](r, theta), theta, theta, theta, theta))/4 end proc

(1)

``

``

 

for w to 1 do for s to 1 do k[w, s] := (int(int(L[w, s](r, theta)*f[w, 1](r, theta), theta = 0 .. 2*Pi), r = 0 .. 1))/(int(int(f[w, 1](r, theta)^2, theta = 0 .. 2*Pi), r = 0 .. 1)); print([w, s] = %) end do end do

[1, 1] = 0.3929199233e-1*(int(0.1005309649e-16*(2329569981.*r*cos(4.700000000*r)^2-0.9913063750e15*r*cos(4.700000000*r)*sin(4.700000000*r)+0.1054581250e21*r*sin(4.700000000*r)^2-328995293.4*r*cos(4.700000000*r)*cosh(4.700000000*r)+0.6999899860e14*r*cos(4.700000000*r)*sinh(4.700000000*r)+0.6999899860e14*r*sin(4.700000000*r)*cosh(4.700000000*r)-0.1489340396e20*r*sin(4.700000000*r)*sinh(4.700000000*r)+1363855.810*r*cosh(4.700000000*r)^2-0.5803641743e12*r*cosh(4.700000000*r)*sinh(4.700000000*r)+0.6174086961e17*r*sinh(4.700000000*r)^2+2982150000.*cos(4.700000000*r)^2-0.1269000000e16*cos(4.700000000*r)*sin(4.700000000*r)+0.1350000000e21*sin(4.700000000*r)^2-816815901.0*cos(4.700000000*r)*cosh(4.700000000*r)+0.1737906172e15*cos(4.700000000*r)*sinh(4.700000000*r)+0.1737906172e15*sin(4.700000000*r)*cosh(4.700000000*r)-0.3697672707e20*sin(4.700000000*r)*sinh(4.700000000*r)+55931812.29*cosh(4.700000000*r)^2-0.2380077119e14*cosh(4.700000000*r)*sinh(4.700000000*r)+0.2531996935e19*sinh(4.700000000*r)^2)/r, r = 0 .. 1))

(2)

``


 

Download approximate_int.mw

 

Hi everybody and thank you all in advance.

This is my question. Suppose I have a list of lists like this:

[[1,2,3],[7,8,9],[13,12,11]]

I want to select all 3rd element from the list of lists and get:

[3,9,11]

Another example:

[1, [2, 3], [4, [5, 6], 7], [8, 3], 9] and select the first element from the list of lists and get:

[1, 2, 4, 8, 9]

Additionally suppose I want to sort a list of lists but base on the 3rd element of every sublist. Example:

From this list:

[[1,2,3],[7,8,2],[13,12,1]] sorted by the  3rd element I would get:

[[13,12,1], [7,8,2], [1,2,3]]

 

So, I am trying to write a method for array interpolation. I have a Matrix that is X by 3, where each column holds specific data (column 1 holds independent data 1, column 2 holds independent data 2, column 3 holds dependent data).

This data comes from a function with 2 independent variables, and I am creating a graph of this function, basically, with both independent variables going from 0 to 1 (approximately 300 values per variable, giving me a matrix with 90k values already). My goal is to use interpolation to get a lot of values in between the points I already calculated.

That being said, I don't know how to use the ArrayInterpolation command to achieve this. I will post my code below if anyone can help me out!

Code:

Interpolate := proc(M::Matrix)
  local i; local j;
  local M1 := Matrix(RowDimension(M),1);
  local M2 := Matrix(RowDimension(M),1);
  local M3 := Matrix(RowDimension(M),1);
  for i from 1 to RowDimension(M) do
    M1(i) := M(i,1);
    M2(i) := M(i,2);
    M3(i) := M(i,3);
  end do;
  print(M1,M2,M3);
  local M4 := Matrix(1000,1);
  local M5 := Matrix(1000,1);
  for j from 1 to 1000 do
    M4(j,1) := 0.001*j;
    M5(j,1) := 0.001*j;
  end do;
  ArrayInterpolation([M1,M2],M3,[M4,M5]);
end proc;

How I can replace  u__0r, theta, t) with f1, 1(r, theta) in attached file.

I want in I have only f1,1] function.

Thanks 


 

````

"f[1, 1](r, theta):=`u__0`(r, theta,t)  "

proc (r, theta) options operator, arrow, function_assign; u__0(r, theta, t) end proc

(1)
``````````

"L[1, 1](r, theta):=-`A__0`*(&PartialD;)/(&PartialD;r) (F*(&PartialD;)/(&PartialD;r)`u__0`(r,theta))-1/(2)*`A__0`*(&PartialD;)/(&PartialD;r) (`K__1`*`u__0`(r,theta))+1/(2)*`A__0`*`K__1`*(&PartialD;)/(&PartialD;r)`u__0`(r,theta)-1/(2)*`A__0`*(&PartialD;)/(&PartialD; r) (`H__1`*`u__0`(r,theta))+1/(2)*`A__0`*`H__1`*(&PartialD;)/(&PartialD;r)`u__0`(r,theta)+`K__3`*`A__0`*`u__0`(r,theta)-1/(2)*`A__0`*(&PartialD;)/(&PartialD; r) (`K__4`*`u__0`(r,theta))+1/(2)*`A__0`*`K__4`*(&PartialD;)/(&PartialD;r)`u__0`(r,theta)+`A__0`*`K__5`*`u__0`(r,theta)-2*`A__0`*(&PartialD;)/(&PartialD; theta) ((`H__2`)/(r)*(&PartialD;)/(&PartialD;theta)`u__0`(r,theta))+(1)/(4)*`A__0`*l^(2)*((&PartialD;)^(2))/(&PartialD; r &PartialD; theta)(mu*((&PartialD;)^(2))/(&PartialD;r &PartialD;theta)`u__0`(r,theta))+(1)/(4)*`A__0`*l^(2)*((&PartialD;)^(2))/(&PartialD;theta^(2))(mu*((&PartialD;)^(2))/(&PartialD; theta^(2))`u__0`(r,theta))+rho*`A__0`*`K__16`*((&PartialD;)^(2))/(&PartialD;t^(2))`u__0`(r,theta);"

proc (r, theta) options operator, arrow, function_assign; -A__0*(diff(F*(diff(u__0(r, theta), r)), r))-(1/2)*A__0*(diff(K__1*u__0(r, theta), r))+(1/2)*A__0*K__1*(diff(u__0(r, theta), r))-(1/2)*A__0*(diff(H__1*u__0(r, theta), r))+(1/2)*A__0*H__1*(diff(u__0(r, theta), r))+K__3*A__0*u__0(r, theta)-(1/2)*A__0*(diff(K__4*u__0(r, theta), r))+(1/2)*A__0*K__4*(diff(u__0(r, theta), r))+A__0*K__5*u__0(r, theta)-2*A__0*(diff(H__2*(diff(u__0(r, theta), theta))/r, theta))+(1/4)*A__0*l^2*(diff(mu*(diff(u__0(r, theta), r, theta)), r, theta))+(1/4)*A__0*l^2*(diff(mu*(diff(u__0(r, theta), theta, theta)), theta, theta))+rho*A__0*K__16*(diff(u__0(r, theta), t, t)) end proc

(2)

``


 

Download replace

 

Foucault’s Pendulum Exploration Using MAPLE18

https://www.ias.ac.in/describe/article/reso/024/06/0653-0659

In this article, we develop the traditional differential equation for Foucault’s pendulum from physical situation and solve it from
standard form. The sublimation of boundary condition eliminates the constants and choice of the local parameters (latitude, pendulum specifications) offers an equation that can be used for a plot followed by animation using MAPLE. The fundamental conceptual components involved in preparing differential equation viz; (i) rotating coordinate system, (ii) rotation of the plane of oscillation and its dependence on the latitude, (iii) effective gravity with latitude, etc., are discussed in detail. The accurate calculations offer quantities up to the sixth decimal point which are used for plotting and animation. This study offers a hands-on experience. Present article offers a know-how to devise a Foucault’s pendulum just by plugging in the latitude of reader’s choice. Students can develop a miniature working model/project of the pendulum.

Hi
i need to find equation of intersection between a plane(Z=0)  and 3d curve like below:

plane :  Z=0

curve:

sqrt(G*(2-G))+(1-G)*(arccos(G-1)+(1/5)*Pi)+k*sqrt(G*(2-G))*cos(sqrt((1+k)/k)*arccos(G-1)+(1/5)*Pi)+sqrt(k/(1+k))*(1-G)*k*sin(sqrt((1+k)/k)*arccos(G-1)+(1/5)*Pi)

I ploted Z=0 plane and that curve . it is like this .
i want equation of the pointed curve(curve equation of intersection between Z=  and curve )in bellow  such as k=f(G) .

best regards

## looking for the coefficients of "A and B"

restart;

t1:=[(-(0.3536776512e-1*(2.999999999*exp(-.1111111111*omega*(2.*cos(theta)+9.))+2.999999999*exp(-.1111111111*omega*(2.*cos(theta)-9.))-2.999999999*exp(-(1/9)*omega*(2*cos(theta)-27))-2.999999999*exp(-.1111111111*omega*(2.*cos(theta)+27.))-2.999999999*exp((1/9)*omega*(2*cos(theta)+27))+2.999999999*exp(.1111111111*omega*(2.*cos(theta)+9.))-2.999999999*exp(.1111111111*omega*(2.*cos(theta)-27.))+2.999999999*exp(.1111111111*omega*(2.*cos(theta)-9.))+2.999999999*exp(.1111111111*omega*(2.*cos(theta)-27.))*omega-2.999999999*exp((1/9)*omega*(2*cos(theta)+27))*omega-9.*exp(.1111111111*omega*(2.*cos(theta)-9.))*omega+9.*exp(.1111111111*omega*(2.*cos(theta)+9.))*omega+12.*exp(.1111111111*omega*(2.*cos(theta)+9.))*omega^2+12.*exp(.1111111111*omega*(2.*cos(theta)-9.))*omega^2-2.999999999*exp(-(1/9)*omega*(2*cos(theta)-27))*omega+9.*exp(-.1111111111*omega*(2.*cos(theta)-9.))*omega-9.*exp(-.1111111111*omega*(2.*cos(theta)+9.))*omega+12.*exp(-.1111111111*omega*(2.*cos(theta)+9.))*omega^2+12.*exp(-.1111111111*omega*(2.*cos(theta)-9.))*omega^2+2.999999999*exp(-.1111111111*omega*(2.*cos(theta)+27.))*omega+.6666666665*exp(.1111111111*omega*(2.*cos(theta)-27.))*omega*cos(theta)+.6666666665*exp((1/9)*omega*(2*cos(theta)+27))*omega*cos(theta)+2.666666667*exp(.1111111111*omega*(2.*cos(theta)-9.))*omega^2*cos(theta)-2.666666667*exp(.1111111111*omega*(2.*cos(theta)+9.))*omega^2*cos(theta)-.6666666665*exp(-.1111111111*omega*(2.*cos(theta)+27.))*omega*cos(theta)-.6666666665*exp(-(1/9)*omega*(2*cos(theta)-27))*omega*cos(theta)+.6666666665*exp(-.1111111111*omega*(2.*cos(theta)-9.))*omega*cos(theta)+.6666666665*exp(-.1111111111*omega*(2.*cos(theta)+9.))*omega*cos(theta)-.6666666665*exp(.1111111111*omega*(2.*cos(theta)+9.))*omega*cos(theta)-2.666666667*exp(-.1111111111*omega*(2.*cos(theta)+9.))*omega^2*cos(theta)+2.666666667*exp(-.1111111111*omega*(2.*cos(theta)-9.))*omega^2*cos(theta)-.6666666665*exp(.1111111111*omega*(2.*cos(theta)-9.))*omega*cos(theta)))*cos((2/9)*omega*sin(theta))/(-16.*omega^2+exp(4*omega)-2.+exp(-4.*omega)))*A-(0.3536776512e-1*(1.570796327*exp(.2222222222*omega*(cos(theta)-9.))-1.570796327*exp(.2222222222*omega*(cos(theta)-18.))-1.570796327*exp(-.2222222222*omega*(cos(theta)-9.))+1.570796327*exp(-(2/9)*omega*cos(theta))+1.570796327*exp((2/9)*omega*cos(theta))-1.570796327*exp(.2222222222*omega*(cos(theta)+9.))+1.570796327*exp(-.2222222222*omega*(cos(theta)+9.))-1.570796327*exp(-.2222222222*omega*(cos(theta)+18.))+4.712388980*exp(-(2/9)*omega*cos(theta))*omega-6.283185307*exp(-(2/9)*omega*cos(theta))*omega^3+4.712388980*exp(-(2/9)*omega*cos(theta))*omega^2+4.712388980*exp((2/9)*omega*cos(theta))*omega-6.283185307*exp((2/9)*omega*cos(theta))*omega^3+4.712388980*exp((2/9)*omega*cos(theta))*omega^2+1.570796327*exp(.2222222222*omega*(cos(theta)-18.))*omega^2+4.712388980*exp(.2222222222*omega*(cos(theta)-9.))*omega^2+1.570796327*exp(.1111111111*omega*(2.*cos(theta)+9.))*sinh(omega)+1.570796327*exp(.1111111111*omega*(2.*cos(theta)-9.))*sinh(omega)-1.570796327*exp(.1111111111*omega*(2.*cos(theta)-27.))*sinh(omega)-1.570796327*exp((1/9)*omega*(2*cos(theta)+27))*sinh(omega)+1.570796327*exp(.2222222222*omega*(cos(theta)-18.))*omega+1.570796327*exp(.2222222222*omega*(cos(theta)+9.))*omega^2+6.283185307*exp(.2222222222*omega*(cos(theta)-9.))*omega^3-1.570796327*exp(.2222222222*omega*(cos(theta)+9.))*omega-4.712388980*exp(.2222222222*omega*(cos(theta)-9.))*omega-1.570796327*exp(-.2222222222*omega*(cos(theta)-9.))*omega-4.712388980*exp(-.2222222222*omega*(cos(theta)+9.))*omega+4.712388980*exp(-.2222222222*omega*(cos(theta)+9.))*omega^2-1.570796327*exp(-(1/9)*omega*(2*cos(theta)-27))*sinh(omega)+1.570796327*exp(-.2222222222*omega*(cos(theta)+18.))*omega+1.570796327*exp(-.1111111111*omega*(2.*cos(theta)-9.))*sinh(omega)+1.570796327*exp(-.2222222222*omega*(cos(theta)-9.))*omega^2+6.283185307*exp(-.2222222222*omega*(cos(theta)+9.))*omega^3-1.570796327*exp(-.1111111111*omega*(2.*cos(theta)+27.))*sinh(omega)+1.570796327*exp(-.1111111111*omega*(2.*cos(theta)+9.))*sinh(omega)+1.570796327*exp(-.2222222222*omega*(cos(theta)+18.))*omega^2+.3490658504*exp(.1111111111*omega*(2.*cos(theta)-27.))*omega^2*cos(theta)*csgn(omega)*sinh(omega)-1.396263401*exp(.1111111111*omega*(2.*cos(theta)+9.))*omega^3*cos(theta)*csgn(omega)*sinh(omega)+1.396263401*exp(.1111111111*omega*(2.*cos(theta)-9.))*omega^3*cos(theta)*csgn(omega)*sinh(omega)-.3490658504*exp(.1111111111*omega*(2.*cos(theta)+9.))*omega^2*cos(theta)*csgn(omega)*sinh(omega)-.3490658504*exp(.1111111111*omega*(2.*cos(theta)-9.))*omega^2*cos(theta)*csgn(omega)*sinh(omega)+1.396263401*exp(.1111111111*omega*(2.*cos(theta)+9.))*omega^2*cos(theta)*csgn(omega)*cosh(omega)-1.396263401*exp(.1111111111*omega*(2.*cos(theta)-9.))*omega^2*cos(theta)*csgn(omega)*cosh(omega)+.3490658504*exp((1/9)*omega*(2*cos(theta)+27))*omega^2*cos(theta)*csgn(omega)*sinh(omega)-.3490658504*exp((1/9)*omega*(2*cos(theta)+27))*omega*cos(theta)*csgn(omega)*cosh(omega)-.3490658504*exp(.1111111111*omega*(2.*cos(theta)-27.))*omega*cos(theta)*csgn(omega)*cosh(omega)+.3490658504*exp(.1111111111*omega*(2.*cos(theta)+9.))*omega*cos(theta)*csgn(omega)*cosh(omega)+.3490658504*exp(.1111111111*omega*(2.*cos(theta)-9.))*omega*cos(theta)*csgn(omega)*cosh(omega)-1.396263401*exp(-.1111111111*omega*(2.*cos(theta)-9.))*omega^2*cos(theta)*csgn(omega)*cosh(omega)+1.396263401*exp(-.1111111111*omega*(2.*cos(theta)+9.))*omega^2*cos(theta)*csgn(omega)*cosh(omega)-.3490658504*exp(-.1111111111*omega*(2.*cos(theta)+27.))*omega^2*cos(theta)*csgn(omega)*sinh(omega)+1.396263401*exp(-.1111111111*omega*(2.*cos(theta)-9.))*omega^3*cos(theta)*csgn(omega)*sinh(omega)-1.396263401*exp(-.1111111111*omega*(2.*cos(theta)+9.))*omega^3*cos(theta)*csgn(omega)*sinh(omega)+.3490658504*exp(-.1111111111*omega*(2.*cos(theta)-9.))*omega^2*cos(theta)*csgn(omega)*sinh(omega)+.3490658504*exp(-.1111111111*omega*(2.*cos(theta)+9.))*omega^2*cos(theta)*csgn(omega)*sinh(omega)-.3490658504*exp(-(1/9)*omega*(2*cos(theta)-27))*omega^2*cos(theta)*csgn(omega)*sinh(omega)+.3490658504*exp(-(1/9)*omega*(2*cos(theta)-27))*omega*cos(theta)*csgn(omega)*cosh(omega)+.3490658504*exp(-.1111111111*omega*(2.*cos(theta)+27.))*omega*cos(theta)*csgn(omega)*cosh(omega)-.3490658504*exp(-.1111111111*omega*(2.*cos(theta)-9.))*omega*cos(theta)*csgn(omega)*cosh(omega)-.3490658504*exp(-.1111111111*omega*(2.*cos(theta)+9.))*omega*cos(theta)*csgn(omega)*cosh(omega)+.3490658504*exp((1/9)*omega*(2*cos(theta)+27))*omega*cos(theta)*sinh(omega)-.3490658504*exp((1/9)*omega*(2*cos(theta)+27))*omega^2*cos(theta)*cosh(omega)+1.396263401*exp(.1111111111*omega*(2.*cos(theta)+9.))*omega^3*cos(theta)*cosh(omega)-1.396263401*exp(.1111111111*omega*(2.*cos(theta)-9.))*omega^3*cos(theta)*cosh(omega)-.3490658504*exp(.1111111111*omega*(2.*cos(theta)-27.))*omega^2*cos(theta)*cosh(omega)-1.396263401*exp(.1111111111*omega*(2.*cos(theta)+9.))*omega^2*cos(theta)*sinh(omega)+1.396263401*exp(.1111111111*omega*(2.*cos(theta)-9.))*omega^2*cos(theta)*sinh(omega)+.3490658504*exp(.1111111111*omega*(2.*cos(theta)+9.))*omega^2*cos(theta)*cosh(omega)+.3490658504*exp(.1111111111*omega*(2.*cos(theta)-9.))*omega^2*cos(theta)*cosh(omega)+1.570796327*exp((1/9)*omega*(2*cos(theta)+27))*csgn(omega)*cosh(omega)*omega-1.570796327*exp(-.1111111111*omega*(2.*cos(theta)+27.))*csgn(omega)*sinh(omega)*omega+4.712388980*exp(-.1111111111*omega*(2.*cos(theta)-9.))*csgn(omega)*sinh(omega)*omega^2-4.712388980*exp(-.1111111111*omega*(2.*cos(theta)+9.))*csgn(omega)*sinh(omega)*omega^2+1.570796327*exp(-.1111111111*omega*(2.*cos(theta)-9.))*csgn(omega)*sinh(omega)*omega+1.570796327*exp(-.1111111111*omega*(2.*cos(theta)+9.))*csgn(omega)*sinh(omega)*omega-4.712388980*exp(-.1111111111*omega*(2.*cos(theta)-9.))*csgn(omega)*cosh(omega)*omega+4.712388980*exp(-.1111111111*omega*(2.*cos(theta)+9.))*csgn(omega)*cosh(omega)*omega-1.570796327*exp(-(1/9)*omega*(2*cos(theta)-27))*csgn(omega)*sinh(omega)*omega-.3490658504*exp(-.1111111111*omega*(2.*cos(theta)+27.))*omega*cos(theta)*sinh(omega)+.3490658504*exp(-.1111111111*omega*(2.*cos(theta)+9.))*omega*cos(theta)*sinh(omega)+.3490658504*exp(-.1111111111*omega*(2.*cos(theta)-9.))*omega*cos(theta)*sinh(omega)-.3490658504*exp(-(1/9)*omega*(2*cos(theta)-27))*omega*cos(theta)*sinh(omega)+6.283185307*exp(-.1111111111*omega*(2.*cos(theta)+9.))*csgn(omega)*sinh(omega)*omega^3-1.570796327*exp(.1111111111*omega*(2.*cos(theta)-27.))*csgn(omega)*cosh(omega)*omega+1.570796327*exp(.1111111111*omega*(2.*cos(theta)-27.))*csgn(omega)*sinh(omega)*omega^2+6.283185307*exp(.1111111111*omega*(2.*cos(theta)+9.))*csgn(omega)*sinh(omega)*omega^3+6.283185307*exp(.1111111111*omega*(2.*cos(theta)-9.))*csgn(omega)*sinh(omega)*omega^3-6.283185307*exp(.1111111111*omega*(2.*cos(theta)+9.))*csgn(omega)*cosh(omega)*omega^2-6.283185307*exp(.1111111111*omega*(2.*cos(theta)-9.))*csgn(omega)*cosh(omega)*omega^2-1.570796327*exp((1/9)*omega*(2*cos(theta)+27))*csgn(omega)*sinh(omega)*omega^2-.3490658504*exp(.1111111111*omega*(2.*cos(theta)-9.))*omega*cos(theta)*sinh(omega)-.3490658504*exp(.1111111111*omega*(2.*cos(theta)+9.))*omega*cos(theta)*sinh(omega)-1.570796327*exp((1/9)*omega*(2*cos(theta)+27))*csgn(omega)*sinh(omega)*omega+.3490658504*exp(.1111111111*omega*(2.*cos(theta)-27.))*omega*cos(theta)*sinh(omega)-6.283185307*exp(-.1111111111*omega*(2.*cos(theta)-9.))*csgn(omega)*cosh(omega)*omega^2-6.283185307*exp(-.1111111111*omega*(2.*cos(theta)+9.))*csgn(omega)*cosh(omega)*omega^2-1.570796327*exp(-(1/9)*omega*(2*cos(theta)-27))*csgn(omega)*sinh(omega)*omega^2+1.570796327*exp(-(1/9)*omega*(2*cos(theta)-27))*csgn(omega)*cosh(omega)*omega-1.570796327*exp(.1111111111*omega*(2.*cos(theta)-27.))*csgn(omega)*sinh(omega)*omega+4.712388980*exp(.1111111111*omega*(2.*cos(theta)+9.))*csgn(omega)*sinh(omega)*omega^2-4.712388980*exp(.1111111111*omega*(2.*cos(theta)-9.))*csgn(omega)*sinh(omega)*omega^2+1.570796327*exp(.1111111111*omega*(2.*cos(theta)+9.))*csgn(omega)*sinh(omega)*omega+1.570796327*exp(.1111111111*omega*(2.*cos(theta)-9.))*csgn(omega)*sinh(omega)*omega-4.712388980*exp(.1111111111*omega*(2.*cos(theta)+9.))*csgn(omega)*cosh(omega)*omega+4.712388980*exp(.1111111111*omega*(2.*cos(theta)-9.))*csgn(omega)*cosh(omega)*omega+.3490658504*exp(-(1/9)*omega*(2*cos(theta)-27))*omega^2*cos(theta)*cosh(omega)+.3490658504*exp(-(2/9)*omega*cos(theta))*omega*cos(theta)+1.745329252*exp(-(2/9)*omega*cos(theta))*omega^2*cos(theta)-1.396263401*exp(-(2/9)*omega*cos(theta))*omega^3*cos(theta)-.3490658504*exp((2/9)*omega*cos(theta))*omega*cos(theta)-1.745329252*exp((2/9)*omega*cos(theta))*omega^2*cos(theta)+1.396263401*exp((2/9)*omega*cos(theta))*omega^3*cos(theta)-6.283185307*exp(.1111111111*omega*(2.*cos(theta)-9.))*cosh(omega)*omega^3-.3490658504*exp(.2222222222*omega*(cos(theta)+9.))*omega^2*cos(theta)+1.745329252*exp(.2222222222*omega*(cos(theta)-9.))*omega^2*cos(theta)-.3490658504*exp(-.2222222222*omega*(cos(theta)+18.))*omega*cos(theta)+1.570796327*exp(-(1/9)*omega*(2*cos(theta)-27))*csgn(omega)*cosh(omega)-6.283185307*exp(.1111111111*omega*(2.*cos(theta)+9.))*cosh(omega)*omega^3+6.283185307*exp(.1111111111*omega*(2.*cos(theta)-9.))*sinh(omega)*omega^2-1.570796327*exp((1/9)*omega*(2*cos(theta)+27))*sinh(omega)*omega-1.570796327*exp(.1111111111*omega*(2.*cos(theta)-27.))*cosh(omega)*omega^2+1.570796327*exp((1/9)*omega*(2*cos(theta)+27))*cosh(omega)*omega^2+1.570796327*exp(.1111111111*omega*(2.*cos(theta)-27.))*sinh(omega)*omega+6.283185307*exp(.1111111111*omega*(2.*cos(theta)+9.))*sinh(omega)*omega^2-1.570796327*exp(-.1111111111*omega*(2.*cos(theta)-9.))*cosh(omega)*omega-1.570796327*exp(-.1111111111*omega*(2.*cos(theta)+9.))*cosh(omega)*omega+.3490658504*exp(.2222222222*omega*(cos(theta)-18.))*omega^2*cos(theta)+1.396263401*exp(.2222222222*omega*(cos(theta)-9.))*omega^3*cos(theta)+.3490658504*exp(.2222222222*omega*(cos(theta)+9.))*omega*cos(theta)-.3490658504*exp(.2222222222*omega*(cos(theta)-9.))*omega*cos(theta)+1.570796327*exp(-(1/9)*omega*(2*cos(theta)-27))*cosh(omega)*omega-4.712388980*exp(-.1111111111*omega*(2.*cos(theta)-9.))*cosh(omega)*omega^2+4.712388980*exp(-.1111111111*omega*(2.*cos(theta)+9.))*cosh(omega)*omega^2+1.570796327*exp(-.1111111111*omega*(2.*cos(theta)+27.))*csgn(omega)*cosh(omega)+1.570796327*exp(-.1111111111*omega*(2.*cos(theta)+27.))*cosh(omega)*omega-1.570796327*exp(-.1111111111*omega*(2.*cos(theta)-9.))*csgn(omega)*cosh(omega)-1.570796327*exp(-.1111111111*omega*(2.*cos(theta)+9.))*csgn(omega)*cosh(omega)+4.712388980*exp(-.1111111111*omega*(2.*cos(theta)-9.))*sinh(omega)*omega-4.712388980*exp(-.1111111111*omega*(2.*cos(theta)+9.))*sinh(omega)*omega+1.570796327*exp((1/9)*omega*(2*cos(theta)+27))*cosh(omega)*omega-4.712388980*exp(.1111111111*omega*(2.*cos(theta)+9.))*cosh(omega)*omega^2+4.712388980*exp(.1111111111*omega*(2.*cos(theta)-9.))*cosh(omega)*omega^2+1.570796327*exp(.1111111111*omega*(2.*cos(theta)-27.))*csgn(omega)*cosh(omega)+1.570796327*exp(.1111111111*omega*(2.*cos(theta)-27.))*cosh(omega)*omega-1.570796327*exp(.1111111111*omega*(2.*cos(theta)+9.))*csgn(omega)*cosh(omega)-1.570796327*exp(.1111111111*omega*(2.*cos(theta)-9.))*csgn(omega)*cosh(omega)+4.712388980*exp(.1111111111*omega*(2.*cos(theta)+9.))*sinh(omega)*omega-4.712388980*exp(.1111111111*omega*(2.*cos(theta)-9.))*sinh(omega)*omega-1.570796327*exp(.1111111111*omega*(2.*cos(theta)+9.))*cosh(omega)*omega-1.570796327*exp(.1111111111*omega*(2.*cos(theta)-9.))*cosh(omega)*omega+1.570796327*exp(-.1111111111*omega*(2.*cos(theta)+27.))*sinh(omega)*omega-1.570796327*exp(-.1111111111*omega*(2.*cos(theta)+27.))*cosh(omega)*omega^2+1.570796327*exp(-(1/9)*omega*(2*cos(theta)-27))*cosh(omega)*omega^2-6.283185307*exp(-.1111111111*omega*(2.*cos(theta)-9.))*cosh(omega)*omega^3-6.283185307*exp(-.1111111111*omega*(2.*cos(theta)+9.))*cosh(omega)*omega^3+.3490658504*exp(-.2222222222*omega*(cos(theta)-9.))*omega^2*cos(theta)-1.745329252*exp(-.2222222222*omega*(cos(theta)+9.))*omega^2*cos(theta)-.3490658504*exp(-.2222222222*omega*(cos(theta)-9.))*omega*cos(theta)+.3490658504*exp(-.2222222222*omega*(cos(theta)+9.))*omega*cos(theta)+6.283185307*exp(-.1111111111*omega*(2.*cos(theta)-9.))*sinh(omega)*omega^2+6.283185307*exp(-.1111111111*omega*(2.*cos(theta)+9.))*sinh(omega)*omega^2-1.570796327*exp(-(1/9)*omega*(2*cos(theta)-27))*sinh(omega)*omega+.3490658504*exp(.2222222222*omega*(cos(theta)-18.))*omega*cos(theta)+1.570796327*exp((1/9)*omega*(2*cos(theta)+27))*csgn(omega)*cosh(omega)-.3490658504*exp(-.2222222222*omega*(cos(theta)+18.))*omega^2*cos(theta)-1.396263401*exp(-.2222222222*omega*(cos(theta)+9.))*omega^3*cos(theta)-1.396263401*exp(-.1111111111*omega*(2.*cos(theta)-9.))*omega^3*cos(theta)*cosh(omega)+1.396263401*exp(-.1111111111*omega*(2.*cos(theta)+9.))*omega^3*cos(theta)*cosh(omega)+.3490658504*exp(-.1111111111*omega*(2.*cos(theta)+27.))*omega^2*cos(theta)*cosh(omega)+1.396263401*exp(-.1111111111*omega*(2.*cos(theta)-9.))*omega^2*cos(theta)*sinh(omega)-1.396263401*exp(-.1111111111*omega*(2.*cos(theta)+9.))*omega^2*cos(theta)*sinh(omega)-.3490658504*exp(-.1111111111*omega*(2.*cos(theta)-9.))*omega^2*cos(theta)*cosh(omega)-.3490658504*exp(-.1111111111*omega*(2.*cos(theta)+9.))*omega^2*cos(theta)*cosh(omega)-1.570796327*exp(-.1111111111*omega*(2.*cos(theta)+27.))*csgn(omega)*cosh(omega)*omega+1.570796327*exp(-.1111111111*omega*(2.*cos(theta)+27.))*csgn(omega)*sinh(omega)*omega^2+6.283185307*exp(-.1111111111*omega*(2.*cos(theta)-9.))*csgn(omega)*sinh(omega)*omega^3))*cos((2/9)*omega*sin(theta))*B/(-16.*omega^2+exp(4*omega)-2.+exp(-4.*omega))-(0.3536776512e-1*(-.5235987758*exp(.2222222222*omega*(cos(theta)-9.))-.5235987758*exp(.2222222222*omega*(cos(theta)-18.))-.5235987758*exp(-.2222222222*omega*(cos(theta)-9.))-.5235987758*exp(-(2/9)*omega*cos(theta))+.5235987758*exp((2/9)*omega*cos(theta))+.5235987758*exp(.2222222222*omega*(cos(theta)+9.))+.5235987758*exp(-.2222222222*omega*(cos(theta)+9.))+.5235987758*exp(-.2222222222*omega*(cos(theta)+18.))-2.094395103*exp(-(2/9)*omega*cos(theta))*omega-2.617993879*exp(-(2/9)*omega*cos(theta))*omega^3-3.665191430*exp(-(2/9)*omega*cos(theta))*omega^2+2.094395103*exp((2/9)*omega*cos(theta))*omega+2.617993879*exp((2/9)*omega*cos(theta))*omega^3+3.665191430*exp((2/9)*omega*cos(theta))*omega^2+.5235987758*exp(.2222222222*omega*(cos(theta)-18.))*omega^2-.5235987758*exp(.2222222222*omega*(cos(theta)-9.))*omega^2+.5235987758*exp(.2222222222*omega*(cos(theta)+9.))*omega^2-2.617993879*exp(.2222222222*omega*(cos(theta)-9.))*omega^3+1.047197552*exp(.2222222222*omega*(cos(theta)+9.))*omega+1.047197552*exp(.2222222222*omega*(cos(theta)-9.))*omega-1.047197552*exp(-.2222222222*omega*(cos(theta)-9.))*omega-1.047197552*exp(-.2222222222*omega*(cos(theta)+9.))*omega+.5235987758*exp(-.2222222222*omega*(cos(theta)+9.))*omega^2-.5235987758*exp(-.2222222222*omega*(cos(theta)-9.))*omega^2+2.617993879*exp(-.2222222222*omega*(cos(theta)+9.))*omega^3-.5235987758*exp(-.2222222222*omega*(cos(theta)+18.))*omega^2-.5235987758*exp(.2222222222*omega*(cos(theta)-18.))*omega^3+.5235987758*exp(.2222222222*omega*(cos(theta)+9.))*omega^3+2.094395103*exp(.2222222222*omega*(cos(theta)-9.))*omega^4+.5235987758*exp(-.2222222222*omega*(cos(theta)+18.))*omega^3-2.094395103*exp(-.2222222222*omega*(cos(theta)+9.))*omega^4-.5235987758*exp(-.2222222222*omega*(cos(theta)-9.))*omega^3-2.094395103*exp(-(2/9)*omega*cos(theta))*omega^4+2.094395103*exp((2/9)*omega*cos(theta))*omega^4-.1163552835*exp(-(2/9)*omega*cos(theta))*omega*cos(theta)-.5817764175*exp(-(2/9)*omega*cos(theta))*omega^2*cos(theta)-.3490658505*exp(-(2/9)*omega*cos(theta))*omega^3*cos(theta)-.1163552835*exp((2/9)*omega*cos(theta))*omega*cos(theta)-.5817764175*exp((2/9)*omega*cos(theta))*omega^2*cos(theta)-.3490658505*exp((2/9)*omega*cos(theta))*omega^3*cos(theta)-.1163552835*exp(.2222222222*omega*(cos(theta)+9.))*omega^2*cos(theta)-.3490658505*exp(.2222222222*omega*(cos(theta)-9.))*omega^2*cos(theta)+.1163552835*exp(-.2222222222*omega*(cos(theta)+18.))*omega*cos(theta)+.1163552835*exp(.2222222222*omega*(cos(theta)-18.))*omega^2*cos(theta)-.3490658505*exp(.2222222222*omega*(cos(theta)-9.))*omega^3*cos(theta)-.1163552835*exp(.2222222222*omega*(cos(theta)+9.))*omega*cos(theta)+.1163552835*exp(.2222222222*omega*(cos(theta)-9.))*omega*cos(theta)-.1163552835*exp(-.2222222222*omega*(cos(theta)-9.))*omega^2*cos(theta)-.3490658505*exp(-.2222222222*omega*(cos(theta)+9.))*omega^2*cos(theta)-.1163552835*exp(-.2222222222*omega*(cos(theta)-9.))*omega*cos(theta)+.1163552835*exp(-.2222222222*omega*(cos(theta)+9.))*omega*cos(theta)+.1163552835*exp(.2222222222*omega*(cos(theta)-18.))*omega*cos(theta)+.1163552835*exp(-.2222222222*omega*(cos(theta)+18.))*omega^2*cos(theta)-.3490658505*exp(-.2222222222*omega*(cos(theta)+9.))*omega^3*cos(theta)-.4654211340*exp(-(2/9)*omega*cos(theta))*omega^4*cos(theta)-.4654211340*exp((2/9)*omega*cos(theta))*omega^4*cos(theta)+.4654211340*exp(-.2222222222*omega*(cos(theta)+9.))*omega^4*cos(theta)-.1163552835*exp(.2222222222*omega*(cos(theta)-18.))*omega^3*cos(theta)-.1163552835*exp(.2222222222*omega*(cos(theta)+9.))*omega^3*cos(theta)+.4654211340*exp(.2222222222*omega*(cos(theta)-9.))*omega^4*cos(theta)-.1163552835*exp(-.2222222222*omega*(cos(theta)+18.))*omega^3*cos(theta)-.1163552835*exp(-.2222222222*omega*(cos(theta)-9.))*omega^3*cos(theta)))*cos((2/9)*omega*sin(theta))*E/(-16.*omega^2+exp(4*omega)-2.+exp(-4.*omega))-(0.3536776512e-1*(-3.141592654*exp(.1111111111*omega*(2.*cos(theta)-9.))*F[2]-.5235987758*exp(.1111111111*omega*(2.*cos(theta)-9.))*G[2]-1.570796327*exp(.2222222222*omega*(cos(theta)-9.))*H[3]-.2617993879*exp(.2222222222*omega*(cos(theta)-9.))*J[3]+1.570796327*exp(.2222222222*omega*(cos(theta)-18.))*H[3]+.2617993879*exp(.2222222222*omega*(cos(theta)-18.))*J[3]+1.570796327*exp(.2222222222*omega*(cos(theta)-27.))*H[3]+.2617993879*exp(.2222222222*omega*(cos(theta)-27.))*J[3]+.2617993879*exp(-(2/9)*omega*cos(theta))*J[3]-.2617993879*exp((2/9)*omega*cos(theta))*J[3]+1.570796327*exp(-(2/9)*omega*cos(theta))*H[3]-1.570796327*exp((2/9)*omega*cos(theta))*H[3]+3.141592654*exp(-.1111111111*omega*(2.*cos(theta)-9.))*F[2]+.5235987758*exp(-.1111111111*omeg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ega*(cos(theta)-18.))*omega^6*J[3]-5.585053608*exp(.1111111111*omega*(2.*cos(theta)-9.))*omega^5*G[2]+50.26548247*exp(-.1111111111*omega*(2.*cos(theta)+27.))*omega^4*F[2]+5.585053608*exp(-.1111111111*omega*(2.*cos(theta)+27.))*omega^5*G[2]-28.27433390*exp(-.2222222222*omega*(cos(theta)+27.))*omega^4*H[3]-2.356194492*exp(-.2222222222*omega*(cos(theta)+27.))*omega^5*J[3]+.7853981636*exp(-.2222222222*omega*(cos(theta)+27.))*omega^3*J[3]+1.396263402*exp(-.1111111111*omega*(2.*cos(theta)-9.))*omega^4*G[2]+1.396263402*exp(-.1111111111*omega*(2.*cos(theta)+45.))*omega^4*G[2]-12.56637062*exp(-.1111111111*omega*(2.*cos(theta)-9.))*omega^2*F[2]+9.424777961*exp(-.2222222222*omega*(cos(theta)+9.))*omega*H[3]+1.570796327*exp(-.2222222222*omega*(cos(theta)+9.))*omega*J[3]-32.98672287*exp(-.2222222222*omega*(cos(theta)+18.))*omega^3*H[3]-.7853981636*exp(-.2222222222*omega*(cos(theta)+18.))*omega^3*J[3]+.5235987758*exp(-.2222222222*omega*(cos(theta)+18.))*omega^2*J[3]+4.188790206*exp(-.2222222222*omega*(cos(theta)+9.))*omega^2*J[3]+17.27875960*exp(-.2222222222*omega*(cos(theta)+18.))*omega^2*H[3]-5.235987758*exp(-.1111111111*omega*(2.*cos(theta)+9.))*omega^2*G[2]+10.99557429*exp(-.2222222222*omega*(cos(theta)+9.))*omega^2*H[3]+.5235987758*exp(-.1111111111*omega*(2.*cos(theta)+45.))*omega*G[2]+12.56637062*exp(-.1111111111*omega*(2.*cos(theta)+9.))*omega^2*F[2]+113.0973355*exp(-.2222222222*omega*(cos(theta)+9.))*omega^5*H[3]+113.0973355*exp(-.2222222222*omega*(cos(theta)+18.))*omega^5*H[3]+1.047197552*exp(-.1111111111*omega*(2.*cos(theta)-9.))*omega^2*G[2]-1.047197552*exp(-.1111111111*omega*(2.*cos(theta)+45.))*omega^2*G[2]-5.585053608*exp(-.1111111111*omega*(2.*cos(theta)+9.))*omega^5*G[2]-50.26548247*exp(-.1111111111*omega*(2.*cos(theta)+9.))*omega^4*F[2]+9.424777964*exp(-.2222222222*omega*(cos(theta)+9.))*omega^6*J[3]+9.424777964*exp(-.2222222222*omega*(cos(theta)+18.))*omega^6*J[3]-3.141592654*exp(-.1111111111*omega*(2.*cos(theta)-9.))*omega*F[2]+1.570796327*exp(-.1111111111*omega*(2.*cos(theta)-9.))*omega*G[2]-9.424777961*exp(-.1111111111*omega*(2.*cos(theta)+45.))*omega*F[2]+2.356194492*exp(-.2222222222*omega*(cos(theta)+9.))*omega^5*J[3]-2.356194492*exp(-.2222222222*omega*(cos(theta)+18.))*omega^5*J[3]-1.396263402*exp(-.1111111111*omega*(2.*cos(theta)+9.))*omega^4*G[2]-65.97344574*exp(-.2222222222*omega*(cos(theta)+9.))*omega^4*H[3]+3.141592654*exp(-.2222222222*omega*(cos(theta)+9.))*omega^4*J[3]-47.12388982*exp(-.2222222222*omega*(cos(theta)+18.))*omega^4*H[3]-3.141592654*exp(-.2222222222*omega*(cos(theta)+18.))*omega^4*J[3]+37.69911184*exp(-.1111111111*omega*(2.*cos(theta)+9.))*omega^3*F[2]-4.188790206*exp(-.1111111111*omega*(2.*cos(theta)+9.))*omega^3*G[2]-23.56194490*exp(-.2222222222*omega*(cos(theta)+9.))*omega^3*H[3]+5.497787146*exp(-.2222222222*omega*(cos(theta)+9.))*omega^3*J[3]+14.13716694*exp(-.2222222222*omega*(cos(theta)+27.))*omega^2*H[3]+4.712388982*exp(-.2222222222*omega*(cos(theta)+27.))*omega^3*H[3]-1.396263402*exp(-.1111111111*omega*(2.*cos(theta)+27.))*omega^4*G[2]-12.56637062*exp(-.1111111111*omega*(2.*cos(theta)+27.))*omega^3*F[2]-4.188790206*exp(-.1111111111*omega*(2.*cos(theta)+27.))*omega^3*G[2]-3.141592654*exp(-.2222222222*omega*(cos(theta)+27.))*omega*H[3]-.5235987758*exp(-.2222222222*omega*(cos(theta)+27.))*omega*J[3]-3.141592654*exp(-.1111111111*omega*(2.*cos(theta)+9.))*omega*F[2]-2.617993879*exp(-.1111111111*omega*(2.*cos(theta)+9.))*omega*G[2]+15.70796327*exp(-.1111111111*omega*(2.*cos(theta)+27.))*omega*F[2]+.5235987758*exp(-.1111111111*omega*(2.*cos(theta)+27.))*omega*G[2]-25.13274122*exp(-.1111111111*omega*(2.*cos(theta)+27.))*omega^2*F[2]+1.047197552*exp(-.1111111111*omega*(2.*cos(theta)+27.))*omega^2*G[2]+12.56637062*exp(-.1111111111*omega*(2.*cos(theta)-9.))*omega^3*F[2]+12.56637062*exp(-.1111111111*omega*(2.*cos(theta)+45.))*omega^3*F[2]+1.047197551*exp(-(2/9)*omega*cos(theta))*omega^2*cos(theta)*H[3]+.1745329253*exp(-(2/9)*omega*cos(theta))*omega^2*cos(theta)*J[3]-5.235987755*exp(-(2/9)*omega*cos(theta))*omega^3*cos(theta)*H[3]+.1745329253*exp(-(2/9)*omega*cos(theta))*omega^3*cos(theta)*J[3]+.5235987760*exp(-(2/9)*omega*cos(theta))*omega^5*cos(theta)*J[3]+6.283185310*exp(-(2/9)*omega*cos(theta))*omega^4*cos(theta)*H[3]+.3490658504*exp(-(2/9)*omega*cos(theta))*omega*cos(theta)*H[3]+0.5817764175e-1*exp(-(2/9)*omega*cos(theta))*omega*cos(theta)*J[3]+1.047197551*exp((2/9)*omega*cos(theta))*omega^2*cos(theta)*H[3]+.1745329253*exp((2/9)*omega*cos(theta))*omega^2*cos(theta)*J[3]-5.235987755*exp((2/9)*omega*cos(theta))*omega^3*cos(theta)*H[3]+.1745329253*exp((2/9)*omega*cos(theta))*omega^3*cos(theta)*J[3]+.5235987760*exp((2/9)*omega*cos(theta))*omega^5*cos(theta)*J[3]+6.283185310*exp((2/9)*omega*cos(theta))*omega^4*cos(theta)*H[3]+.3490658504*exp((2/9)*omega*cos(theta))*omega*cos(theta)*H[3]+0.5817764175e-1*exp((2/9)*omega*cos(theta))*omega*cos(theta)*J[3]+6.283185307*exp(-(2/9)*omega*cos(theta))*omega*H[3]+1.047197552*exp(-(2/9)*omega*cos(theta))*omega*J[3]+.7853981636*exp(-(2/9)*omega*cos(theta))*omega^3*J[3]-4.712388980*exp(-(2/9)*omega*cos(theta))*omega^2*H[3]+1.570796327*exp(-(2/9)*omega*cos(theta))*omega^2*J[3]-23.56194490*exp(-(2/9)*omega*cos(theta))*omega^3*H[3]+2.356194492*exp(-(2/9)*omega*cos(theta))*omega^5*J[3]+28.27433390*exp(-(2/9)*omega*cos(theta))*omega^4*H[3]-6.283185307*exp((2/9)*omega*cos(theta))*omega*H[3]-1.047197552*exp((2/9)*omega*cos(theta))*omega*J[3]-.7853981636*exp((2/9)*omega*cos(theta))*omega^3*J[3]+4.712388980*exp((2/9)*omega*cos(theta))*omega^2*H[3]-1.570796327*exp((2/9)*omega*cos(theta))*omega^2*J[3]+23.56194490*exp((2/9)*omega*cos(theta))*omega^3*H[3]-2.356194492*exp((2/9)*omega*cos(theta))*omega^5*J[3]-28.27433390*exp((2/9)*omega*cos(theta))*omega^4*H[3]+2.792526803*exp(.1111111111*omega*(2.*cos(theta)+9.))*omega^2*cos(theta)*F[2]-.2327105670*exp(.1111111111*omega*(2.*cos(theta)+9.))*omega^2*cos(theta)*G[2]+.3490658504*exp(.2222222222*omega*(cos(theta)-18.))*omega^2*cos(theta)*H[3]+2.792526804*exp(.1111111111*omega*(2.*cos(theta)-45.))*omega^3*cos(theta)*F[2]-25.13274123*exp(-.2222222222*omega*(cos(theta)+18.))*omega^5*cos(theta)*H[3]-.5235987760*exp(-.2222222222*omega*(cos(theta)+18.))*omega^5*cos(theta)*J[3]-11.17010721*exp(-.1111111111*omega*(2.*cos(theta)+9.))*omega^4*cos(theta)*F[2]+.3102807560*exp(-.1111111111*omega*(2.*cos(theta)+9.))*omega^4*cos(theta)*G[2]-27.22713633*exp(-.2222222222*omega*(cos(theta)+9.))*omega^4*cos(theta)*H[3]+.6981317013*exp(-.2222222222*omega*(cos(theta)+9.))*omega^4*cos(theta)*J[3]+.5235987760*exp(-.2222222222*omega*(cos(theta)+27.))*omega^5*cos(theta)*J[3]-1.047197551*exp(-.2222222222*omega*(cos(theta)+27.))*omega^3*cos(theta)*H[3]-.1745329253*exp(-.2222222222*omega*(cos(theta)+27.))*omega^3*cos(theta)*J[3]+6.283185310*exp(-.2222222222*omega*(cos(theta)+27.))*omega^4*cos(theta)*H[3]-1.241123024*exp(-.1111111111*omega*(2.*cos(theta)+27.))*omega^5*cos(theta)*G[2]-11.17010721*exp(-.1111111111*omega*(2.*cos(theta)+27.))*omega^4*cos(theta)*F[2]-.3102807560*exp(-.1111111111*omega*(2.*cos(theta)+27.))*omega^4*cos(theta)*G[2]-1.047197551*exp(-.2222222222*omega*(cos(theta)+27.))*omega^2*cos(theta)*H[3]-.1745329253*exp(-.2222222222*omega*(cos(theta)+27.))*omega^2*cos(theta)*J[3]-2.792526803*exp(-.1111111111*omega*(2.*cos(theta)+9.))*omega^2*cos(theta)*F[2]-.6981317013*exp(-.1111111111*omega*(2.*cos(theta)+9.))*omega^2*cos(theta)*G[2]+5.585053605*exp(-.1111111111*omega*(2.*cos(theta)+27.))*omega^2*cos(theta)*F[2]+.3490658504*exp(-.2222222222*omega*(cos(theta)+18.))*omega^2*cos(theta)*H[3]+0.5817764175e-1*exp(-.2222222222*omega*(cos(theta)+18.))*omega^2*cos(theta)*J[3]+2.094395103*exp(-.2222222222*omega*(cos(theta)+9.))*omega^6*cos(theta)*J[3]-2.094395103*exp(-.2222222222*omega*(cos(theta)+18.))*omega^6*cos(theta)*J[3]-1.241123024*exp(-.1111111111*omega*(2.*cos(theta)+9.))*omega^5*cos(theta)*G[2]+25.13274123*exp(-.2222222222*omega*(cos(theta)+9.))*omega^5*cos(theta)*H[3]-.5235987760*exp(-.2222222222*omega*(cos(theta)+9.))*omega^5*cos(theta)*J[3]-.6981317013*exp(-.1111111111*omega*(2.*cos(theta)+27.))*omega*cos(theta)*F[2]-.1163552835*exp(-.1111111111*omega*(2.*cos(theta)+27.))*omega*cos(theta)*G[2]-2.792526803*exp(-.1111111111*omega*(2.*cos(theta)-9.))*omega^2*cos(theta)*F[2]+.2327105670*exp(-.1111111111*omega*(2.*cos(theta)-9.))*omega^2*cos(theta)*G[2]-.3490658504*exp(-.2222222222*omega*(cos(theta)+18.))*omega*cos(theta)*H[3]-0.5817764175e-1*exp(-.2222222222*omega*(cos(theta)+18.))*omega*cos(theta)*J[3]-.3490658504*exp(-.2222222222*omega*(cos(theta)+27.))*omega*cos(theta)*H[3]-0.5817764175e-1*exp(-.2222222222*omega*(cos(theta)+27.))*omega*cos(theta)*J[3]-.6981317013*exp(-.1111111111*omega*(2.*cos(theta)+9.))*omega*cos(theta)*F[2]-.1163552835*exp(-.1111111111*omega*(2.*cos(theta)+9.))*omega*cos(theta)*G[2]+.3490658504*exp(-.2222222222*omega*(cos(theta)+9.))*omega*cos(theta)*H[3]+0.5817764175e-1*exp(-.2222222222*omega*(cos(theta)+9.))*omega*cos(theta)*J[3]-.1163552835*exp(.1111111111*omega*(2.*cos(theta)+9.))*omega*cos(theta)*G[2]-.6981317013*exp(.1111111111*omega*(2.*cos(theta)-45.))*omega*cos(theta)*F[2]+2.792526804*exp(-.1111111111*omega*(2.*cos(theta)-9.))*omega^3*cos(theta)*F[2]+9.424777960*exp(.2222222222*omega*(cos(theta)-18.))*omega^3*cos(theta)*H[3]-2.094395101*exp(.2222222222*omega*(cos(theta)-18.))*omega^4*cos(theta)*H[3]+.6981317013*exp(.2222222222*omega*(cos(theta)-18.))*omega^4*cos(theta)*J[3]+2.443460953*exp(.2222222222*omega*(cos(theta)-9.))*omega^2*cos(theta)*H[3]+.4072434923*exp(.2222222222*omega*(cos(theta)-9.))*omega^2*cos(theta)*J[3]-2.792526804*exp(.1111111111*omega*(2.*cos(theta)+9.))*omega^3*cos(theta)*F[2]-.6981317013*exp(.1111111111*omega*(2.*cos(theta)+9.))*omega*cos(theta)*F[2]-.1745329253*exp(.2222222222*omega*(cos(theta)-27.))*omega^2*cos(theta)*J[3]+2.792526803*exp(.1111111111*omega*(2.*cos(theta)-9.))*omega^2*cos(theta)*F[2]+.6981317013*exp(.1111111111*omega*(2.*cos(theta)-9.))*omega^2*cos(theta)*G[2]-5.585053605*exp(.1111111111*omega*(2.*cos(theta)-27.))*omega^2*cos(theta)*F[2]-.2327105670*exp(.1111111111*omega*(2.*cos(theta)-27.))*omega^2*cos(theta)*G[2]+2.792526803*exp(.1111111111*omega*(2.*cos(theta)-27.))*omega^3*cos(theta)*F[2]-.9308422680*exp(.1111111111*omega*(2.*cos(theta)-27.))*omega^3*cos(theta)*G[2]+.3102807560*exp(.1111111111*omega*(2.*cos(theta)-45.))*omega^4*cos(theta)*G[2]-.3102807560*exp(.1111111111*omega*(2.*cos(theta)+9.))*omega^4*cos(theta)*G[2]-.2327105670*exp(.1111111111*omega*(2.*cos(theta)-45.))*omega^2*cos(theta)*G[2]-13.96263402*exp(.1111111111*omega*(2.*cos(theta)-9.))*omega^3*cos(theta)*F[2]+.9308422680*exp(.1111111111*omega*(2.*cos(theta)-9.))*omega^3*cos(theta)*G[2]+5.235987755*exp(.2222222222*omega*(cos(theta)-9.))*omega^3*cos(theta)*H[3]+.5235987760*exp(.2222222222*omega*(cos(theta)-18.))*omega^3*cos(theta)*J[3]+.8726646260*exp(.2222222222*omega*(cos(theta)-9.))*omega^3*cos(theta)*J[3]+2.094395103*exp(.2222222222*omega*(cos(theta)-9.))*omega^6*cos(theta)*J[3]-2.094395103*exp(.2222222222*omega*(cos(theta)-18.))*omega^6*cos(theta)*J[3]+1.241123024*exp(.1111111111*omega*(2.*cos(theta)-9.))*omega^5*cos(theta)*G[2]+25.13274123*exp(.2222222222*omega*(cos(theta)-9.))*omega^5*cos(theta)*H[3]-.5235987760*exp(.2222222222*omega*(cos(theta)-9.))*omega^5*cos(theta)*J[3]-25.13274123*exp(.2222222222*omega*(cos(theta)-18.))*omega^5*cos(theta)*H[3]-.5235987760*exp(.2222222222*omega*(cos(theta)-18.))*omega^5*cos(theta)*J[3]+11.17010721*exp(.1111111111*omega*(2.*cos(theta)-9.))*omega^4*cos(theta)*F[2]-.3102807560*exp(.1111111111*omega*(2.*cos(theta)-9.))*omega^4*cos(theta)*G[2]-27.22713633*exp(.2222222222*omega*(cos(theta)-9.))*omega^4*cos(theta)*H[3]+.6981317013*exp(.2222222222*omega*(cos(theta)-9.))*omega^4*cos(theta)*J[3]+.5235987760*exp(.2222222222*omega*(cos(theta)-27.))*omega^5*cos(theta)*J[3]-1.047197551*exp(.2222222222*omega*(cos(theta)-27.))*omega^3*cos(theta)*H[3]-.1745329253*exp(.2222222222*omega*(cos(theta)-27.))*omega^3*cos(theta)*J[3]+6.283185310*exp(.2222222222*omega*(cos(theta)-27.))*omega^4*cos(theta)*H[3]+1.241123024*exp(.1111111111*omega*(2.*cos(theta)-27.))*omega^5*cos(theta)*G[2]+11.17010721*exp(.1111111111*omega*(2.*cos(theta)-27.))*omega^4*cos(theta)*F[2]+.3102807560*exp(.1111111111*omega*(2.*cos(theta)-27.))*omega^4*cos(theta)*G[2]-1.047197551*exp(.2222222222*omega*(cos(theta)-27.))*omega^2*cos(theta)*H[3]-2.792526804*exp(-.1111111111*omega*(2.*cos(theta)+45.))*omega^3*cos(theta)*F[2]+.8726646260*exp(-.2222222222*omega*(cos(theta)+9.))*omega^3*cos(theta)*J[3]+.6981317013*exp(-.1111111111*omega*(2.*cos(theta)-9.))*omega*cos(theta)*F[2]+.1163552835*exp(-.1111111111*omega*(2.*cos(theta)-9.))*omega*cos(theta)*G[2]+.6981317013*exp(-.1111111111*omega*(2.*cos(theta)+45.))*omega*cos(theta)*F[2]+.1163552835*exp(-.1111111111*omega*(2.*cos(theta)+45.))*omega*cos(theta)*G[2]-.1163552835*exp(.1111111111*omega*(2.*cos(theta)-45.))*omega*cos(theta)*G[2]+.2327105670*exp(-.1111111111*omega*(2.*cos(theta)+27.))*omega^2*cos(theta)*G[2]-2.792526803*exp(-.1111111111*omega*(2.*cos(theta)+27.))*omega^3*cos(theta)*F[2]+.9308422680*exp(-.1111111111*omega*(2.*cos(theta)+27.))*omega^3*cos(theta)*G[2]-.3102807560*exp(-.1111111111*omega*(2.*cos(theta)+45.))*omega^4*cos(theta)*G[2]+.3102807560*exp(-.1111111111*omega*(2.*cos(theta)-9.))*omega^4*cos(theta)*G[2]+.2327105670*exp(-.1111111111*omega*(2.*cos(theta)+45.))*omega^2*cos(theta)*G[2]+13.96263402*exp(-.1111111111*omega*(2.*cos(theta)+9.))*omega^3*cos(theta)*F[2]-.9308422680*exp(-.1111111111*omega*(2.*cos(theta)+9.))*omega^3*cos(theta)*G[2]+5.235987755*exp(-.2222222222*omega*(cos(theta)+9.))*omega^3*cos(theta)*H[3]+.5235987760*exp(-.2222222222*omega*(cos(theta)+18.))*omega^3*cos(theta)*J[3]+.6981317013*exp(.1111111111*omega*(2.*cos(theta)-27.))*omega*cos(theta)*F[2]+.1163552835*exp(.1111111111*omega*(2.*cos(theta)-27.))*omega*cos(theta)*G[2]+9.424777960*exp(-.2222222222*omega*(cos(theta)+18.))*omega^3*cos(theta)*H[3]-2.094395101*exp(-.2222222222*omega*(cos(theta)+18.))*omega^4*cos(theta)*H[3]+.6981317013*exp(-.2222222222*omega*(cos(theta)+18.))*omega^4*cos(theta)*J[3]+2.443460953*exp(-.2222222222*omega*(cos(theta)+9.))*omega^2*cos(theta)*H[3]+.4072434923*exp(-.2222222222*omega*(cos(theta)+9.))*omega^2*cos(theta)*J[3]+0.5817764175e-1*exp(.2222222222*omega*(cos(theta)-18.))*omega^2*cos(theta)*J[3]+.6981317013*exp(.1111111111*omega*(2.*cos(theta)-9.))*omega*cos(theta)*F[2]+.1163552835*exp(.1111111111*omega*(2.*cos(theta)-9.))*omega*cos(theta)*G[2]+.3490658504*exp(.2222222222*omega*(cos(theta)-9.))*omega*cos(theta)*H[3]+0.5817764175e-1*exp(.2222222222*omega*(cos(theta)-9.))*omega*cos(theta)*J[3]-.3490658504*exp(.2222222222*omega*(cos(theta)-18.))*omega*cos(theta)*H[3]-0.5817764175e-1*exp(.2222222222*omega*(cos(theta)-18.))*omega*cos(theta)*J[3]-.3490658504*exp(.2222222222*omega*(cos(theta)-27.))*omega*cos(theta)*H[3]-0.5817764175e-1*exp(.2222222222*omega*(cos(theta)-27.))*omega*cos(theta)*J[3]))*cos((2/9)*omega*sin(theta))/(-16.*omega^2+exp(4*omega)-2.+exp(-4.*omega))]:
t:=coeff(t1,A);
 

 

## but i'm getting the error "Error, unable to compute coeff". Please help me!

 

 

How I can differential with respect to the constant Amnr], Bmnr], Cmnr]


 

e := mu*(((cosh(eta)-cos(theta))/a)^2*(diff(`U__&eta;`(eta, `&varphi;`, theta), eta, eta))+(1-cosh(eta)*cos(theta))*(cosh(eta)-cos(theta))*(diff(`U__&eta;`(eta, `&varphi;`, theta), eta))/(a^2*sinh(eta))+2*sinh(eta)*(cosh(eta)-cos(theta))*(diff(`U__&theta;`(eta, `&varphi;`, theta), theta))/a^2)

T := proc () options operator, arrow; rho*omega^2*(int(int(int((u(eta, `&varphi;`, theta)^2+v(eta, `&varphi;`, theta)^2+w(eta, `&varphi;`, theta)^2)*a^3*sinh(eta)/(cosh(eta)-cos(`&varphi;`))^3, theta = a .. b), eta = c .. d), `&varphi;` = e .. f)) end proc

u__trial := proc (eta, `&varphi;`, theta, M, N) options operator, arrow; sum(sum(sum(A[m, n, r]*u[m, n, r](eta, `&varphi;`, theta), n = 1 .. N), m = 1 .. M), r = 1 .. R) end proc; v__trial := proc (eta, `&varphi;`, theta, M, N) options operator, arrow; sum(sum(sum(B[m, n, r]*v[m, n, r](eta, `&varphi;`, theta), n = 1 .. N), m = 1 .. M), r = 1 .. R) end proc; w__trial := proc (eta, `&varphi;`, theta, M, N) options operator, arrow; sum(sum(sum(C[m, n, r]*w[m, n, r](eta, `&varphi;`, theta), n = 1 .. N), m = 1 .. M), r = 1 .. R) end proc

proc (eta, varphi, theta, M, N) options operator, arrow; sum(sum(sum(C[m, n, r]*w[m, n, r](eta, varphi, theta), n = 1 .. N), m = 1 .. M), r = 1 .. R) end proc

(1)

L := e-T()

"(&PartialD;)/(&PartialD; A[m,n,r])L"

``

``

``

``

``

``

``

``


 

Download

 

How I can plot torus structure in the following code instead of cylindrical.

Thanks.


 

"U[1,6](x,theta):=0.03215257166 (sin(-2.350000000+9.400000000 x)-0.1369508410 sinh(-2.350000000+9.400000000 x)) cos(6 theta):"

 

 

with(plots)

[animate, animate3d, animatecurve, arrow, changecoords, complexplot, complexplot3d, conformal, conformal3d, contourplot, contourplot3d, coordplot, coordplot3d, densityplot, display, dualaxisplot, fieldplot, fieldplot3d, gradplot, gradplot3d, implicitplot, implicitplot3d, inequal, interactive, interactiveparams, intersectplot, listcontplot, listcontplot3d, listdensityplot, listplot, listplot3d, loglogplot, logplot, matrixplot, multiple, odeplot, pareto, plotcompare, pointplot, pointplot3d, polarplot, polygonplot, polygonplot3d, polyhedra_supported, polyhedraplot, rootlocus, semilogplot, setcolors, setoptions, setoptions3d, shadebetween, spacecurve, sparsematrixplot, surfdata, textplot, textplot3d, tubeplot]

(1)

cylinderplot(U[1, 6](x, theta)-.1, theta = 0 .. 2*Pi, x = 0 .. .5, grid = [50, 50])

 

torus

torus

(2)

``


 

Download toro.mw

 

 

\Hello,

How I can solve this algebraic to find unknowns ABCD?

I want to gain ABCD automatically without input the coefficients in rule by hand.

Because I should run the code for many input data

Thanks


 

restart;

l:=0.5;a:=0.1; rho:=2700;h:=.0005;
E:=72.4*10^9;v:= 0.3;
n:=6;
m:=1;

AD:=10;
mu:=(2*a*2.35)/l;
nu:=sin(mu*l/(2*a))/sinh(mu*l/(2*a)); omega[m,n]:= 3067.173621;

.5

 

.1

 

2700

 

0.5e-3

 

0.7240000000e11

 

.3

 

6

 

1

 

10

 

.9400000000

 

.1369508410

 

3067.173621

(1)

 

E:=1:k[1,1]:=-5.660173062*10^10:k[1,2]:=-2.8552873062*10^10:k[1,3]:=-8.68528173062*10^10:k[1,4]:=-7.6788528173062*10^10:k[1,5]:=-1.52568528173062*10^10:k[2,1]:=-15.660173062*10^10:k[2,2]:=-21.8552873062*10^10:k[2,3]:=-18.68528173062*10^10:k[2,4]:=-71.6788528173062*10^10:k[2,5]:=-10.52568528173062*10^10:
k[3,1]:=-5.65257260173062*10^10:k[3,2]:=-27.8552552873062*10^10:k[3,3]:=-81.6854428173062*10^10:k[3,4]:=-9.67858528173062*10^10:k[3,5]:=-3.52568528173062*10^10:
k[4,1]:=-51.111660173062*10^10:k[4,2]:=-21.811552873062*10^10:k[4,3]:=-18.68528173062*10^10:k[4,4]:=-17.6788528173062*10^10:k[4,5]:=-11.52568528173062*10^10:
k[5,1]:=-6.660173062*10^10:k[5,2]:=-61.852873062*10^10:k[5,3]:=-82.68528173062*10^10:k[5,4]:=-72.6788528173062*10^10:k[5,5]:=-21.52568528173062*10^10

-0.2152568528e12

(2)

 

 

S:=(Matrix([[rho*h*omega[m,n]^2+k[1, 1],k[1,2],k[1,3],k[1,4]],[k[2,1],rho*h*omega[m,n]^2+k[2,2],k[2,3],k[2,4]],[k[3,1],k[3,2],k[3,3]+rho*h*omega[m,n]^2,k[3,4]],[k[4,1],k[4,2],k[4,3],k[4,4]+rho*h*omega[m,n]^2]])).(Vector(1..4,[[A],[B],[C],[D]]))=-E*(Vector(1..4,[k[1,5],k[2, 5],k[3,5],k[4,5]]));

(Vector(4, {(1) = -0.5658903042e11*A-0.2855287306e11*B-0.8685281731e11*C-0.7678852817e11*D, (2) = -0.1566017306e12*A-0.2185401729e12*B-0.1868528173e12*C-0.7167885282e12*D, (3) = -0.5652572602e11*A-0.2785525529e12*B-0.8168417280e12*C-0.9678585282e11*D, (4) = -0.5111166017e12*A-0.2181155287e12*B-0.1868528173e12*C-0.1767758280e12*D})) = (Vector(4, {(1) = 0.1525685282e11, (2) = 0.1052568528e12, (3) = 0.3525685282e11, (4) = 0.1152568528e12}))

(3)

``


 

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