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Table and sketches inside table not shown in full ...

Asked by: Ramakrishnan 399
document export
June 19 2019
1  0

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

subs do not work well ...

Asked by: torabi 90
differentiation subs duplicate-question
June 19 2019
0  1

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

Error in Matrix - cannot determine if true or fals...

Asked by: JD423 5
matrix precalculus
June 19 2019
1  8

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

ApproximateInt- numerical-simpson...

Asked by: 9009134 110
integration numeric approximateint
June 19 2019
0  6

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

 

Select from a lists of lists...

Asked by: Fernando Ismael 60
sort map list
June 18 2019
2  4

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]]

 

help me to created two animate in one graph...

Asked by: permanoon123 165
animate plotting
June 18 2019
0  2

both_of_them.mw

General Procedure For Array Interpolation ...

Asked by: TheAkashain 25
interpolation curvefitting arrayinterpolation
June 18 2019
2  1

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;

replace function u__0(r, theta, t) with f[1, 1](r,...

Asked by: 9009134 110
substitution
June 18 2019
0  1

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

 

how to find equation of intersection between a pla...

Asked by: love-algebra 25
June 18 2019
3  8

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

How to extract the coefficients ? ...

Asked by: Gourav 10
coeff coefficients
June 18 2019
0  2

## 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 constan...

Asked by: torabi 90
differentiation
June 17 2019
0  12

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

 

plot torus strucures...

Asked by: 9009134 110
plotting torus
June 17 2019
0  14

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

 

 

solving algebraic equations...

Asked by: fatemeh1090 65
solve
June 17 2019
1  2

\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)
> 

``


 

Download solve.mw

 

 

 

Why does Maple not plot?...

Asked by: Sofi_jf 5
plot ode dsolve
June 17 2019
1  1


 

Setup

 
> 

restart; with(plots); C := setcolors()

> 

dBarrel := .33

> 

ABarrel := Pi*((1/2)*dBarrel)^2

> 

`&rho;Water` := 997

> 

VBarrel := 0.6e-2

0.6e-2

(1.1)
> 

hBarrel := VBarrel/ABarrel

0.7015093909e-1

(1.2)
> 

VWater := 0.15e-2

> 

VAir := VBarrel-VWater

0.45e-2

(1.3)
> 

h0 := VWater/ABarrel

0.1753773477e-1

(1.4)
> 

rhoAir := 1.164

> 

g := 9.81

> 

rhoAtmos := 1.01325*10^5

> 

rhoWater := 997

> 

dNozzle := 0.1e-2

> 

ANozzle := Pi*((1/2)*dNozzle)^2

> 

Cd := .4

Boyle's law

 
> 

eq1 := p1*V1 = p2*V2

p1*V1 = p2*V2

(2.1)
> 

p1 := pBegin

pBegin

(2.2)
> 

V1 := VAir

0.45e-2

(2.3)
> 

V2 := (hBarrel-h(t))*ABarrel

0.6000000000e-2-0.8552986001e-1*h(t)

(2.4)
> 

pa := solve(eq1, p2)

-450000000.*pBegin/(8552986001.*h(t)-600000000.)

(2.5)

Conservation of Energy

 

db is much smaller then da, herfore va is neglected.

> 

eq2 := pa/rhoWater+g.h(t) = rhoAtmos/rhoWater+(1/2)*vb^2

-451354.0622*pBegin/(8552986001.*h(t)-600000000.)+9.81*h(t) = 101.6298897+(1/2)*vb^2

(3.1)
> 

vbTheoretical := solve(eq2, vb)

0.4472135955e-3*((8552986001.*h(t)-600000000.)*(0.8390479267e18*h(t)^2-0.8751250239e19*h(t)-0.4513540622e13*pBegin+0.6097793382e18))^(1/2)/(8552986001.*h(t)-600000000.), -0.4472135955e-3*((8552986001.*h(t)-600000000.)*(0.8390479267e18*h(t)^2-0.8751250239e19*h(t)-0.4513540622e13*pBegin+0.6097793382e18))^(1/2)/(8552986001.*h(t)-600000000.)

 (3.2)
> 

vbWithDischarge := Cd.vbTheoretical[2]

-0.1788854382e-3*((8552986001.*h(t)-600000000.)*(0.8390479267e18*h(t)^2-0.8751250239e19*h(t)-0.4513540622e13*pBegin+0.6097793382e18))^(1/2)/(8552986001.*h(t)-600000000.)

 (3.3)
> 

NULL

Conservation of Mass

 
> 

eq3 := -`&rho;Water`*ATank*(diff(h(t), t)) = `&rho;Water`*ANozzle*vbWithDischarge

-997*ATank*(diff(h(t), t)) = -0.1400748058e-6*((8552986001.*h(t)-600000000.)*(0.8390479267e18*h(t)^2-0.8751250239e19*h(t)-0.4513540622e13*pBegin+0.6097793382e18))^(1/2)/(8552986001.*h(t)-600000000.)

 (4.1)
> 

ics := h(0) = h0

> 

sol := dsolve({eq3, ics}, type = numeric, output = listprocedure)

Warning, The use of global variables in numerical ODE problems is deprecated, and will be removed in a future release. Use the 'parameters' argument instead (see ?dsolve,numeric,parameters)

 

[t = proc (t) local _res, _dat, _solnproc, _xout, _ndsol, _pars, _i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; if 1 < nargs then error "invalid input: too many arguments" end if; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then _xout := evalf[_EnvDSNumericSaveDigits](t) else _xout := evalf(t) end if; _dat := Array(1..4, {(1) = proc (_xin) local _xout, _dtbl, _dat, _vmap, _x0, _y0, _val, _dig, _n, _ne, _nd, _nv, _pars, _ini, _par, _i, _j, _k, _src; option `Copyright (c) 2002 by Waterloo Maple Inc. All rights reserved.`; table( [( "complex" ) = false ] ) _xout := _xin; _pars := [ATank = ATank, pBegin = pBegin]; _dtbl := array( 1 .. 4, [( 1 ) = (array( 1 .. 26, [( 1 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 2 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 3 ) = ([0, 0, 0, Array(1..0, 1..2, {}, datatype = float[8], order = C_order)]), ( 4 ) = (Array(1..63, {(1) = 1, (2) = 1, (3) = 0, (4) = 0, (5) = 2, (6) = 0, (7) = 0, (8) = 0, (9) = 0, (10) = 0, (11) = 0, (12) = 0, (13) = 0, (14) = 0, (15) = 0, (16) = 0, (17) = 0, (18) = 0, (19) = 30000, (20) = 0, (21) = 0, (22) = 1, (23) = 4, (24) = 0, (25) = 1, (26) = 15, (27) = 1, (28) = 0, (29) = 1, (30) = 3, (31) = 3, (32) = 0, (33) = 1, (34) = 0, (35) = 0, (36) = 0, (37) = 0, (38) = 0, (39) = 0, (40) = 0, (41) = 0, (42) = 0, (43) = 1, (44) = 0, (45) = 0, (46) = 0, (47) = 0, (48) = 0, (49) = 0, (50) = 50, (51) = 1, (52) = 0, (53) = 0, (54) = 0, (55) = 0, (56) = 0, (57) = 0, (58) = 0, (59) = 10000, (60) = 0, (61) = 1000, (62) = 0, (63) = 0}, datatype = integer[8])), ( 5 ) = (Array(1..28, {(1) = .0, (2) = 0.10e-5, (3) = .0, (4) = 0.500001e-14, (5) = .0, (6) = .0, (7) = .0, (8) = 0.10e-5, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = 1.0, (14) = .0, (15) = .49999999999999, (16) = .0, (17) = 1.0, (18) = 1.0, (19) = .0, (20) = .0, (21) = 1.0, (22) = 1.0, (23) = .0, (24) = .0, (25) = 0.10e-14, (26) = .0, (27) = .0, (28) = .0}, datatype = float[8], order = C_order)), ( 6 ) = (Array(1..3, {(1) = 0.1753773477e-1, (2) = Float(undefined), (3) = Float(undefined)})), ( 7 ) = ([Array(1..4, 1..7, {(1, 1) = .0, (1, 2) = .203125, (1, 3) = .3046875, (1, 4) = .75, (1, 5) = .8125, (1, 6) = .40625, (1, 7) = .8125, (2, 1) = 0.6378173828125e-1, (2, 2) = .0, (2, 3) = .279296875, (2, 4) = .27237892150878906, (2, 5) = -0.9686851501464844e-1, (2, 6) = 0.1956939697265625e-1, (2, 7) = .5381584167480469, (3, 1) = 0.31890869140625e-1, (3, 2) = .0, (3, 3) = -.34375, (3, 4) = -.335235595703125, (3, 5) = .2296142578125, (3, 6) = .41748046875, (3, 7) = 11.480712890625, (4, 1) = 0.9710520505905151e-1, (4, 2) = .0, (4, 3) = .40350341796875, (4, 4) = 0.20297467708587646e-1, (4, 5) = -0.6054282188415527e-2, (4, 6) = -0.4770040512084961e-1, (4, 7) = .77858567237854}, datatype = float[8], order = C_order), Array(1..6, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = 1.0, (2, 1) = .25, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = 1.0, (3, 1) = .1875, (3, 2) = .5625, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = 2.0, (4, 1) = .23583984375, (4, 2) = -.87890625, (4, 3) = .890625, (4, 4) = .0, (4, 5) = .0, (4, 6) = .2681884765625, (5, 1) = .1272735595703125, (5, 2) = -.5009765625, (5, 3) = .44921875, (5, 4) = -0.128936767578125e-1, (5, 5) = .0, (5, 6) = 0.626220703125e-1, (6, 1) = -0.927734375e-1, (6, 2) = .626220703125, (6, 3) = -.4326171875, (6, 4) = .1418304443359375, (6, 5) = -0.861053466796875e-1, (6, 6) = .3131103515625}, datatype = float[8], order = C_order), Array(1..6, {(1) = .0, (2) = .386, (3) = .21, (4) = .63, (5) = 1.0, (6) = 1.0}, datatype = float[8], order = C_order), Array(1..6, {(1) = .25, (2) = -.1043, (3) = .1035, (4) = -0.362e-1, (5) = .0, (6) = .0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 1.544, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = .9466785280815533, (3, 2) = .25570116989825814, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = 3.3148251870684886, (4, 2) = 2.896124015972123, (4, 3) = .9986419139977808, (4, 4) = .0, (4, 5) = .0, (5, 1) = 1.2212245092262748, (5, 2) = 6.019134481287752, (5, 3) = 12.537083329320874, (5, 4) = -.687886036105895, (5, 5) = .0, (6, 1) = 1.2212245092262748, (6, 2) = 6.019134481287752, (6, 3) = 12.537083329320874, (6, 4) = -.687886036105895, (6, 5) = 1.0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = -5.6688, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = -2.4300933568337584, (3, 2) = -.20635991570891224, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = -.10735290581452621, (4, 2) = -9.594562251021896, (4, 3) = -20.470286148096154, (4, 4) = .0, (4, 5) = .0, (5, 1) = 7.496443313968615, (5, 2) = -10.246804314641219, (5, 3) = -33.99990352819906, (5, 4) = 11.708908932061595, (5, 5) = .0, (6, 1) = 8.083246795922411, (6, 2) = -7.981132988062785, (6, 3) = -31.52159432874373, (6, 4) = 16.319305431231363, (6, 5) = -6.0588182388340535}, datatype = float[8], order = C_order), Array(1..3, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 10.126235083446911, (2, 2) = -7.487995877607633, (2, 3) = -34.800918615557414, (2, 4) = -7.9927717075687275, (2, 5) = 1.0251377232956207, (3, 1) = -.6762803392806898, (3, 2) = 6.087714651678606, (3, 3) = 16.43084320892463, (3, 4) = 24.767225114183653, (3, 5) = -6.5943891257167815}, datatype = float[8], order = C_order)]), ( 9 ) = ([Array(1..1, {(1) = .1}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..1, {(1, 1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..1, {(1, 1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..1, {(1, 1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = 0}, datatype = integer[8]), Array(1..3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8], order = C_order), Array(1..3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8], order = C_order), Array(1..3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8], order = C_order), Array(1..3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order)]), ( 8 ) = ([Array(1..3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8], order = C_order), Array(1..3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), 0, 0]), ( 11 ) = (Array(1..6, 0..1, {(1, 1) = .0, (2, 0) = .0, (2, 1) = .0, (3, 0) = .0, (3, 1) = .0, (4, 0) = .0, (4, 1) = .0, (5, 0) = .0, (5, 1) = .0, (6, 0) = .0, (6, 1) = .0}, datatype = float[8], order = C_order)), ( 10 ) = ([proc (N, X, Y, YP) option `[Y[1] = h(t)]`; if (8552986001.*Y[1]-600000000.)*(0.8390479267e18*Y[1]^2-0.8751250239e19*Y[1]-0.4513540622e13*Y[3]+0.6097793382e18) < 0 then YP[1] := undefined; return 0 end if; YP[1] := 0.14049629468405215647e-9*evalf(((8552986001.*Y[1]-600000000.)*(0.8390479267e18*Y[1]^2-0.8751250239e19*Y[1]-0.4513540622e13*Y[3]+0.6097793382e18))^(1/2))/((8552986001.*Y[1]-600000000.)*Y[2]); 0 end proc, -1, 0, 0, 0, 0, 0, 0]), ( 13 ) = (), ( 12 ) = (), ( 15 ) = ("rkf45"), ( 14 ) = ([2, table( [( 2, "local" ) = pBegin, ( 2, "name" ) = pBegin, ( 1, "value" ) = undefined, ( 1, "local" ) = ATank, ( 1, "name" ) = ATank, ( 2, "value" ) = undefined ] )]), ( 18 ) = ([]), ( 19 ) = (0), ( 16 ) = ([0, 0, 0, []]), ( 17 ) = ([proc (N, X, Y, YP) option `[Y[1] = h(t)]`; if (8552986001.*Y[1]-600000000.)*(0.8390479267e18*Y[1]^2-0.8751250239e19*Y[1]-0.4513540622e13*Y[3]+0.6097793382e18) < 0 then YP[1] := undefined; return 0 end if; YP[1] := 0.14049629468405215647e-9*evalf(((8552986001.*Y[1]-600000000.)*(0.8390479267e18*Y[1]^2-0.8751250239e19*Y[1]-0.4513540622e13*Y[3]+0.6097793382e18))^(1/2))/((8552986001.*Y[1]-600000000.)*Y[2]); 0 end proc, -1, 0, 0, 0, 0, 0, 0]), ( 22 ) = (0), ( 23 ) = (0), ( 20 ) = ([]), ( 21 ) = (0), ( 26 ) = (Array(1..0, {})), ( 25 ) = (Array(1..0, {})), ( 24 ) = (0) ] )) ] ); _y0 := Array(0..3, {(1) = 0., (2) = 0.1753773477e-1, (3) = undefined}); _vmap := array( 1 .. 1, [( 1 ) = (1) ] ); _x0 := _dtbl[1][5][5]; _n := _dtbl[1][4][1]; _ne := _dtbl[1][4][3]; _nd := _dtbl[1][4][4]; _nv := _dtbl[1][4][16]; if not type(_xout, 'numeric') then if member(_xout, ["start", "left", "right"]) then if _Env_smart_dsolve_numeric = true or _dtbl[1][4][10] = 1 then if _xout = "left" then if type(_dtbl[2], 'table') then return _dtbl[2][5][1] end if elif _xout = "right" then if type(_dtbl[3], 'table') then return _dtbl[3][5][1] end if end if end if; return _dtbl[1][5][5] elif _xout = "method" then return _dtbl[1][15] elif _xout = "storage" then return evalb(_dtbl[1][4][10] = 1) elif _xout = "leftdata" then if not type(_dtbl[2], 'array') then return NULL else return eval(_dtbl[2]) end if elif _xout = "rightdata" then if not type(_dtbl[3], 'array') then return NULL else return eval(_dtbl[3]) end if elif _xout = "enginedata" then return eval(_dtbl[1]) elif _xout = "enginereset" then _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); return NULL elif _xout = "initial" then return procname(_y0[0]) elif _xout = "laxtol" then return _dtbl[`if`(member(_dtbl[4], {2, 3}), _dtbl[4], 1)][5][18] elif _xout = "numfun" then return `if`(member(_dtbl[4], {2, 3}), _dtbl[_dtbl[4]][4][18], 0) elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return procname(_y0[0]), [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "last" then if _dtbl[4] <> 2 and _dtbl[4] <> 3 or _x0-_dtbl[_dtbl[4]][5][1] = 0. then error "no information is available on last computed point" else _xout := _dtbl[_dtbl[4]][5][1] end if elif _xout = "function" then if _dtbl[1][4][33]-2. = 0 then return eval(_dtbl[1][10], 1) else return eval(_dtbl[1][10][1], 1) end if elif _xout = "map" then return copy(_vmap) elif type(_xin, `=`) and type(rhs(_xin), 'list') and member(lhs(_xin), {"initial", "parameters", "initial_and_parameters"}) then _ini, _par := [], []; if lhs(_xin) = "initial" then _ini := rhs(_xin) elif lhs(_xin) = "parameters" then _par := rhs(_xin) elif select(type, rhs(_xin), `=`) <> [] then _par, _ini := selectremove(type, rhs(_xin), `=`) elif nops(rhs(_xin)) < nops(_pars)+1 then error "insufficient data for specification of initial and parameters" else _par := rhs(_xin)[-nops(_pars) .. -1]; _ini := rhs(_xin)[1 .. -nops(_pars)-1] end if; _xout := lhs(_xout); if _par <> [] then `dsolve/numeric/process_parameters`(_n, _pars, _par, _y0) end if; if _ini <> [] then `dsolve/numeric/process_initial`(_n-_ne, _ini, _y0, _pars, _vmap) end if; `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars); if _Env_smart_dsolve_numeric = true and type(_y0[0], 'numeric') and _dtbl[1][4][10] <> 1 then procname("right") := _y0[0]; procname("left") := _y0[0] end if; if _xout = "initial" then return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)] elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] else return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)], [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] end if elif _xin = "eventstop" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then return 0 end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 100 and 100 <= _dtbl[5-_i][4][9] then _i := 5-_i; _dtbl[4] := _i; _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) elif 100 <= _dtbl[_i][4][9] then _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) else return 0 end if elif _xin = "eventstatus" then if _nv = 0 then error "this solution has no events" end if; _i := [selectremove(proc (a) options operator, arrow; _dtbl[1][3][1][a, 7] = 1 end proc, {seq(_j, _j = 1 .. round(_dtbl[1][3][1][_nv+1, 1]))})]; return ':-enabled' = _i[1], ':-disabled' = _i[2] elif _xin = "eventclear" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then error "no events to clear" end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 100 and 100 < _dtbl[5-_i][4][9] then _dtbl[4] := 5-_i; _i := 5-_i end if; if _dtbl[_i][4][9] < 100 then error "no events to clear" elif _nv < _dtbl[_i][4][9]-100 then error "event error condition cannot be cleared" else _j := _dtbl[_i][4][9]-100; if irem(round(_dtbl[_i][3][1][_j, 4]), 2) = 1 then error "retriggerable events cannot be cleared" end if; _j := round(_dtbl[_i][3][1][_j, 1]); for _k to _nv do if _dtbl[_i][3][1][_k, 1] = _j then if _dtbl[_i][3][1][_k, 2] = 3 then error "range events cannot be cleared" end if; _dtbl[_i][3][1][_k, 8] := _dtbl[_i][3][1][_nv+1, 8] end if end do; _dtbl[_i][4][17] := 0; _dtbl[_i][4][9] := 0; if _dtbl[1][4][10] = 1 then if _i = 2 then try procname(procname("left")) catch: end try else try procname(procname("right")) catch: end try end if end if end if; return elif type(_xin, `=`) and member(lhs(_xin), {"eventdisable", "eventenable"}) then if _nv = 0 then error "this solution has no events" end if; if type(rhs(_xin), {('list')('posint'), ('set')('posint')}) then _i := {op(rhs(_xin))} elif type(rhs(_xin), 'posint') then _i := {rhs(_xin)} else error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; if select(proc (a) options operator, arrow; _nv < a end proc, _i) <> {} then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _k := {}; for _j to _nv do if member(round(_dtbl[1][3][1][_j, 1]), _i) then _k := `union`(_k, {_j}) end if end do; _i := _k; if lhs(_xin) = "eventdisable" then _dtbl[4] := 0; _j := [evalb(assigned(_dtbl[2]) and member(_dtbl[2][4][17], _i)), evalb(assigned(_dtbl[3]) and member(_dtbl[3][4][17], _i))]; for _k in _i do _dtbl[1][3][1][_k, 7] := 0; if assigned(_dtbl[2]) then _dtbl[2][3][1][_k, 7] := 0 end if; if assigned(_dtbl[3]) then _dtbl[3][3][1][_k, 7] := 0 end if end do; if _j[1] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[2][3][4][_k, 1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to defined init `, _dtbl[2][3][4][_k, 1]); _dtbl[2][3][1][_k, 8] := _dtbl[2][3][4][_k, 1] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to rate hysteresis init `, _dtbl[2][5][24]); _dtbl[2][3][1][_k, 8] := _dtbl[2][5][24] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to initial init `, _x0); _dtbl[2][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to fireinitial init `, _x0-1); _dtbl[2][3][1][_k, 8] := _x0-1 end if end do; _dtbl[2][4][17] := 0; _dtbl[2][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("left")) end if end if; if _j[2] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[3][3][4][_k, 2], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to defined init `, _dtbl[3][3][4][_k, 2]); _dtbl[3][3][1][_k, 8] := _dtbl[3][3][4][_k, 2] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to rate hysteresis init `, _dtbl[3][5][24]); _dtbl[3][3][1][_k, 8] := _dtbl[3][5][24] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to initial init `, _x0); _dtbl[3][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to fireinitial init `, _x0+1); _dtbl[3][3][1][_k, 8] := _x0+1 end if end do; _dtbl[3][4][17] := 0; _dtbl[3][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("right")) end if end if else for _k in _i do _dtbl[1][3][1][_k, 7] := 1 end do; _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); _dtbl[4] := 0; if _dtbl[1][4][10] = 1 then if _x0 <= procname("right") then try procname(procname("right")) catch: end try end if; if procname("left") <= _x0 then try procname(procname("left")) catch: end try end if end if end if; return elif type(_xin, `=`) and lhs(_xin) = "eventfired" then if not type(rhs(_xin), 'list') then error "'eventfired' must be specified as a list" end if; if _nv = 0 then error "this solution has no events" end if; if _dtbl[4] <> 2 and _dtbl[4] <> 3 then error "'direction' must be set prior to calling/setting 'eventfired'" end if; _i := _dtbl[4]; _val := NULL; if not assigned(_EnvEventRetriggerWarned) then _EnvEventRetriggerWarned := false end if; for _k in rhs(_xin) do if type(_k, 'integer') then _src := _k elif type(_k, 'integer' = 'anything') and type(evalf(rhs(_k)), 'numeric') then _k := lhs(_k) = evalf[max(Digits, 18)](rhs(_k)); _src := lhs(_k) else error "'eventfired' entry is not valid: %1", _k end if; if _src < 1 or round(_dtbl[1][3][1][_nv+1, 1]) < _src then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _src := {seq(`if`(_dtbl[1][3][1][_j, 1]-_src = 0., _j, NULL), _j = 1 .. _nv)}; if nops(_src) <> 1 then error "'eventfired' can only be set/queried for root-finding events and time/interval events" end if; _src := _src[1]; if _dtbl[1][3][1][_src, 2] <> 0. and _dtbl[1][3][1][_src, 2]-2. <> 0. then error "'eventfired' can only be set/queried for root-finding events and time/interval events" elif irem(round(_dtbl[1][3][1][_src, 4]), 2) = 1 then if _EnvEventRetriggerWarned = false then WARNING(`'eventfired' has no effect on events that retrigger`) end if; _EnvEventRetriggerWarned := true end if; if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then _val := _val, undefined elif type(_dtbl[_i][3][4][_src, _i-1], 'undefined') or _i = 2 and _dtbl[2][3][1][_src, 8] < _dtbl[2][3][4][_src, 1] or _i = 3 and _dtbl[3][3][4][_src, 2] < _dtbl[3][3][1][_src, 8] then _val := _val, _dtbl[_i][3][1][_src, 8] else _val := _val, _dtbl[_i][3][4][_src, _i-1] end if; if type(_k, `=`) then if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then error "cannot set event code for a rate hysteresis event" end if; userinfo(3, {'events', 'eventreset'}, `manual set event code `, _src, ` to value `, rhs(_k)); _dtbl[_i][3][1][_src, 8] := rhs(_k); _dtbl[_i][3][4][_src, _i-1] := rhs(_k) end if end do; return [_val] elif type(_xin, `=`) and lhs(_xin) = "direction" then if not member(rhs(_xin), {-1, 1, ':-left', ':-right'}) then error "'direction' must be specified as either '1' or 'right' (positive) or '-1' or 'left' (negative)" end if; _src := `if`(_dtbl[4] = 2, -1, `if`(_dtbl[4] = 3, 1, undefined)); _i := `if`(member(rhs(_xin), {1, ':-right'}), 3, 2); _dtbl[4] := _i; _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if; return _src elif _xin = "eventcount" then if _dtbl[1][3][1] = 0 or _dtbl[4] <> 2 and _dtbl[4] <> 3 then return 0 else return round(_dtbl[_dtbl[4]][3][1][_nv+1, 12]) end if else return "procname" end if end if; if _xout = _x0 then return [_x0, seq(evalf(_dtbl[1][6][_vmap[_i]]), _i = 1 .. _n-_ne)] end if; _i := `if`(_x0 <= _xout, 3, 2); if _xin = "last" and 0 < _dtbl[_i][4][9] and _dtbl[_i][4][9] < 100 then _dat := eval(_dtbl[_i], 2); _j := _dat[4][20]; return [_dat[11][_j, 0], seq(_dat[11][_j, _vmap[_i]], _i = 1 .. _n-_ne-_nd), seq(_dat[8][1][_vmap[_i]], _i = _n-_ne-_nd+1 .. _n-_ne)] end if; if not type(_dtbl[_i], 'array') then _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if end if; if _xin <> "last" then if 0 < 2 then if `dsolve/numeric/checkglobals`(op(_dtbl[1][14]), _pars, _n, _y0) then `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars, _i) end if end if; if _dtbl[1][4][7] = 0 then error "parameters must be initialized before solution can be computed" end if end if; _dat := eval(_dtbl[_i], 2); _dtbl[4] := _i; try _src := `dsolve/numeric/SC/IVPrun`(_dat, _xout) catch: userinfo(2, `dsolve/debug`, print(`Exception in solnproc:`, [lastexception][2 .. -1])); error end try; if _dat[17] <> _dtbl[1][17] then _dtbl[1][17] := _dat[17]; _dtbl[1][10] := _dat[10] end if; if _src = 0 and 100 < _dat[4][9] then _val := _dat[3][1][_nv+1, 8] else _val := _dat[11][_dat[4][20], 0] end if; if _src <> 0 or _dat[4][9] <= 0 then _dtbl[1][5][1] := _xout else _dtbl[1][5][1] := _val end if; if _i = 3 and _val < _xout then Rounding := -infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further right of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further right of %1, maxfun limit exceeded (see <a href='http://www.maplesoft.com/support/help/search.aspx?term=dsolve,maxfun' target='_new'>?dsolve,maxfun</a> for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further right of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further right of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif _dat[4][9] = 6 then error "cannot evaluate the solution further right of %1, cannot downgrade delay storage for problems with delay derivative order > 1, try increasing delaypts", evalf[8](_val) elif _dat[4][9] = 10 then error "cannot evaluate the solution further right of %1, interrupt requested", evalf[8](_val) elif 100 < _dat[4][9] then if _dat[4][9]-100 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further right of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-100, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further right of %1", evalf[8](_val) end if elif _i = 2 and _xout < _val then Rounding := infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further left of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further left of %1, maxfun limit exceeded (see <a href='http://www.maplesoft.com/support/help/search.aspx?term=dsolve,maxfun' target='_new'>?dsolve,maxfun</a> for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further left of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further left of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif _dat[4][9] = 6 then error "cannot evaluate the solution further left of %1, cannot downgrade delay storage for problems with delay derivative order > 1, try increasing delaypts", evalf[8](_val) elif _dat[4][9] = 10 then error "cannot evaluate the solution further right of %1, interrupt requested", evalf[8](_val) elif 100 < _dat[4][9] then if _dat[4][9]-100 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further left of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-100, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further left of %1", evalf[8](_val) end if end if; if _EnvInFsolve = true then _dig := _dat[4][26]; if type(_EnvDSNumericSaveDigits, 'posint') then _dat[4][26] := _EnvDSNumericSaveDigits else _dat[4][26] := Digits end if; _Env_dsolve_SC_native := true; if _dat[4][25] = 1 then _i := 1; _dat[4][25] := 2 else _i := _dat[4][25] end if; _val := `dsolve/numeric/SC/IVPval`(_dat, _xout, _src); _dat[4][25] := _i; _dat[4][26] := _dig; [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] else Digits := _dat[4][26]; _val := `dsolve/numeric/SC/IVPval`(eval(_dat, 2), _xout, _src); [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] end if end proc, (2) = Array(1..2, {(1) = 18446745843388771334, (2) = 18446745843388771510}), (3) = [t, h(t)], (4) = [ATank = ATank, pBegin = pBegin]}); _solnproc := _dat[1]; _pars := map(rhs, _dat[4]); if not type(_xout, 'numeric') then if member(t, ["start", 'start', "method", 'method', "left", 'left', "right", 'right', "leftdata", "rightdata", "enginedata", "eventstop", 'eventstop', "eventclear", 'eventclear', "eventstatus", 'eventstatus', "eventcount", 'eventcount', "laxtol", 'laxtol', "numfun", 'numfun', NULL]) then _res := _solnproc(convert(t, 'string')); if 1 < nops([_res]) then return _res elif type(_res, 'array') then return eval(_res, 1) elif _res <> "procname" then return _res end if elif member(t, ["last", 'last', "initial", 'initial', NULL]) then _res := _solnproc(convert(t, 'string')); if type(_res, 'list') then return _res[1] else return NULL end if elif member(t, ["parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(t, 'string'); _res := _solnproc(_xout); if _xout = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [_res[1], seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] end if elif type(_xout, `=`) and member(lhs(_xout), ["initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(lhs(t), 'string') = rhs(t); if lhs(_xout) = "initial" then if type(rhs(_xout), 'list') then _res := _solnproc(_xout) else _res := _solnproc("initial" = ["single", 1, rhs(_xout)]) end if elif not type(rhs(_xout), 'list') then error "initial and/or parameter values must be specified in a list" elif lhs(_xout) = "initial_and_parameters" and nops(rhs(_xout)) = nops(_pars)+1 then _res := _solnproc(lhs(_xout) = ["single", 1, op(rhs(_xout))]) else _res := _solnproc(_xout) end if; if lhs(_xout) = "initial" then return _res[1] elif lhs(_xout) = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [_res[1], seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] end if elif type(_xout, `=`) and member(lhs(_xout), ["eventdisable", 'eventdisable', "eventenable", 'eventenable', "eventfired", 'eventfired', "direction", 'direction', NULL]) then return _solnproc(convert(lhs(t), 'string') = rhs(t)) elif _xout = "solnprocedure" then return eval(_solnproc) elif _xout = "sysvars" then return _dat[3] end if; if procname <> unknown then return ('procname')(t) else _ndsol := 1; _ndsol := `tools/gensym`("t"); eval(FromInert(_Inert_FUNCTION(_Inert_NAME("assign"), _Inert_EXPSEQ(ToInert(_ndsol), _Inert_VERBATIM(pointto(_dat[2][1])))))); return FromInert(_Inert_FUNCTION(ToInert(_ndsol), _Inert_EXPSEQ(ToInert(t)))) end if end if; try _res := _solnproc(_xout); _res[1] catch: error end try end proc, h(t) = proc (t) local _res, _dat, _solnproc, _xout, _ndsol, _pars, _i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; if 1 < nargs then error "invalid input: too many arguments" end if; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then _xout := evalf[_EnvDSNumericSaveDigits](t) else _xout := evalf(t) end if; _dat := Array(1..4, {(1) = proc (_xin) local _xout, _dtbl, _dat, _vmap, _x0, _y0, _val, _dig, _n, _ne, _nd, _nv, _pars, _ini, _par, _i, _j, _k, _src; option `Copyright (c) 2002 by Waterloo Maple Inc. All rights reserved.`; table( [( "complex" ) = false ] ) _xout := _xin; _pars := [ATank = ATank, pBegin = pBegin]; _dtbl := array( 1 .. 4, [( 1 ) = (array( 1 .. 26, [( 1 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 2 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 3 ) = ([0, 0, 0, Array(1..0, 1..2, {}, datatype = float[8], order = C_order)]), ( 4 ) = (Array(1..63, {(1) = 1, (2) = 1, (3) = 0, (4) = 0, (5) = 2, (6) = 0, (7) = 0, (8) = 0, (9) = 0, (10) = 0, (11) = 0, (12) = 0, (13) = 0, (14) = 0, (15) = 0, (16) = 0, (17) = 0, (18) = 0, (19) = 30000, (20) = 0, (21) = 0, (22) = 1, (23) = 4, (24) = 0, (25) = 1, (26) = 15, (27) = 1, (28) = 0, (29) = 1, (30) = 3, (31) = 3, (32) = 0, (33) = 1, (34) = 0, (35) = 0, (36) = 0, (37) = 0, (38) = 0, (39) = 0, (40) = 0, (41) = 0, (42) = 0, (43) = 1, (44) = 0, (45) = 0, (46) = 0, (47) = 0, (48) = 0, (49) = 0, (50) = 50, (51) = 1, (52) = 0, (53) = 0, (54) = 0, (55) = 0, (56) = 0, (57) = 0, (58) = 0, (59) = 10000, (60) = 0, (61) = 1000, (62) = 0, (63) = 0}, datatype = integer[8])), ( 5 ) = (Array(1..28, {(1) = .0, (2) = 0.10e-5, (3) = .0, (4) = 0.500001e-14, (5) = .0, (6) = .0, (7) = .0, (8) = 0.10e-5, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = 1.0, (14) = .0, (15) = .49999999999999, (16) = .0, (17) = 1.0, (18) = 1.0, (19) = .0, (20) = .0, (21) = 1.0, (22) = 1.0, (23) = .0, (24) = .0, (25) = 0.10e-14, (26) = .0, (27) = .0, (28) = .0}, datatype = float[8], order = C_order)), ( 6 ) = (Array(1..3, {(1) = 0.1753773477e-1, (2) = Float(undefined), (3) = Float(undefined)})), ( 7 ) = ([Array(1..4, 1..7, {(1, 1) = .0, (1, 2) = .203125, (1, 3) = .3046875, (1, 4) = .75, (1, 5) = .8125, (1, 6) = .40625, (1, 7) = .8125, (2, 1) = 0.6378173828125e-1, (2, 2) = .0, (2, 3) = .279296875, (2, 4) = .27237892150878906, (2, 5) = -0.9686851501464844e-1, (2, 6) = 0.1956939697265625e-1, (2, 7) = .5381584167480469, (3, 1) = 0.31890869140625e-1, (3, 2) = .0, (3, 3) = -.34375, (3, 4) = -.335235595703125, (3, 5) = .2296142578125, (3, 6) = .41748046875, (3, 7) = 11.480712890625, (4, 1) = 0.9710520505905151e-1, (4, 2) = .0, (4, 3) = .40350341796875, (4, 4) = 0.20297467708587646e-1, (4, 5) = -0.6054282188415527e-2, (4, 6) = -0.4770040512084961e-1, (4, 7) = .77858567237854}, datatype = float[8], order = C_order), Array(1..6, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = 1.0, (2, 1) = .25, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = 1.0, (3, 1) = .1875, (3, 2) = .5625, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = 2.0, (4, 1) = .23583984375, (4, 2) = -.87890625, (4, 3) = .890625, (4, 4) = .0, (4, 5) = .0, (4, 6) = .2681884765625, (5, 1) = .1272735595703125, (5, 2) = -.5009765625, (5, 3) = .44921875, (5, 4) = -0.128936767578125e-1, (5, 5) = .0, (5, 6) = 0.626220703125e-1, (6, 1) = -0.927734375e-1, (6, 2) = .626220703125, (6, 3) = -.4326171875, (6, 4) = .1418304443359375, (6, 5) = -0.861053466796875e-1, (6, 6) = .3131103515625}, datatype = float[8], order = C_order), Array(1..6, {(1) = .0, (2) = .386, (3) = .21, (4) = .63, (5) = 1.0, (6) = 1.0}, datatype = float[8], order = C_order), Array(1..6, {(1) = .25, (2) = -.1043, (3) = .1035, (4) = -0.362e-1, (5) = .0, (6) = .0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 1.544, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = .9466785280815533, (3, 2) = .25570116989825814, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = 3.3148251870684886, (4, 2) = 2.896124015972123, (4, 3) = .9986419139977808, (4, 4) = .0, (4, 5) = .0, (5, 1) = 1.2212245092262748, (5, 2) = 6.019134481287752, (5, 3) = 12.537083329320874, (5, 4) = -.687886036105895, (5, 5) = .0, (6, 1) = 1.2212245092262748, (6, 2) = 6.019134481287752, (6, 3) = 12.537083329320874, (6, 4) = -.687886036105895, (6, 5) = 1.0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = -5.6688, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = -2.4300933568337584, (3, 2) = -.20635991570891224, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = -.10735290581452621, (4, 2) = -9.594562251021896, (4, 3) = -20.470286148096154, (4, 4) = .0, (4, 5) = .0, (5, 1) = 7.496443313968615, (5, 2) = -10.246804314641219, (5, 3) = -33.99990352819906, (5, 4) = 11.708908932061595, (5, 5) = .0, (6, 1) = 8.083246795922411, (6, 2) = -7.981132988062785, (6, 3) = -31.52159432874373, (6, 4) = 16.319305431231363, (6, 5) = -6.0588182388340535}, datatype = float[8], order = C_order), Array(1..3, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 10.126235083446911, (2, 2) = -7.487995877607633, (2, 3) = -34.800918615557414, (2, 4) = -7.9927717075687275, (2, 5) = 1.0251377232956207, (3, 1) = -.6762803392806898, (3, 2) = 6.087714651678606, (3, 3) = 16.43084320892463, (3, 4) = 24.767225114183653, (3, 5) = -6.5943891257167815}, datatype = float[8], order = C_order)]), ( 9 ) = ([Array(1..1, {(1) = .1}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..1, {(1, 1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..1, {(1, 1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..1, {(1, 1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = 0}, datatype = integer[8]), Array(1..3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8], order = C_order), Array(1..3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8], order = C_order), Array(1..3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8], order = C_order), Array(1..3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order)]), ( 8 ) = ([Array(1..3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8], order = C_order), Array(1..3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), 0, 0]), ( 11 ) = (Array(1..6, 0..1, {(1, 1) = .0, (2, 0) = .0, (2, 1) = .0, (3, 0) = .0, (3, 1) = .0, (4, 0) = .0, (4, 1) = .0, (5, 0) = .0, (5, 1) = .0, (6, 0) = .0, (6, 1) = .0}, datatype = float[8], order = C_order)), ( 10 ) = ([proc (N, X, Y, YP) option `[Y[1] = h(t)]`; if (8552986001.*Y[1]-600000000.)*(0.8390479267e18*Y[1]^2-0.8751250239e19*Y[1]-0.4513540622e13*Y[3]+0.6097793382e18) < 0 then YP[1] := undefined; return 0 end if; YP[1] := 0.14049629468405215647e-9*evalf(((8552986001.*Y[1]-600000000.)*(0.8390479267e18*Y[1]^2-0.8751250239e19*Y[1]-0.4513540622e13*Y[3]+0.6097793382e18))^(1/2))/((8552986001.*Y[1]-600000000.)*Y[2]); 0 end proc, -1, 0, 0, 0, 0, 0, 0]), ( 13 ) = (), ( 12 ) = (), ( 15 ) = ("rkf45"), ( 14 ) = ([2, table( [( 2, "local" ) = pBegin, ( 2, "name" ) = pBegin, ( 1, "value" ) = undefined, ( 1, "local" ) = ATank, ( 1, "name" ) = ATank, ( 2, "value" ) = undefined ] )]), ( 18 ) = ([]), ( 19 ) = (0), ( 16 ) = ([0, 0, 0, []]), ( 17 ) = ([proc (N, X, Y, YP) option `[Y[1] = h(t)]`; if (8552986001.*Y[1]-600000000.)*(0.8390479267e18*Y[1]^2-0.8751250239e19*Y[1]-0.4513540622e13*Y[3]+0.6097793382e18) < 0 then YP[1] := undefined; return 0 end if; YP[1] := 0.14049629468405215647e-9*evalf(((8552986001.*Y[1]-600000000.)*(0.8390479267e18*Y[1]^2-0.8751250239e19*Y[1]-0.4513540622e13*Y[3]+0.6097793382e18))^(1/2))/((8552986001.*Y[1]-600000000.)*Y[2]); 0 end proc, -1, 0, 0, 0, 0, 0, 0]), ( 22 ) = (0), ( 23 ) = (0), ( 20 ) = ([]), ( 21 ) = (0), ( 26 ) = (Array(1..0, {})), ( 25 ) = (Array(1..0, {})), ( 24 ) = (0) ] )) ] ); _y0 := Array(0..3, {(1) = 0., (2) = 0.1753773477e-1, (3) = undefined}); _vmap := array( 1 .. 1, [( 1 ) = (1) ] ); _x0 := _dtbl[1][5][5]; _n := _dtbl[1][4][1]; _ne := _dtbl[1][4][3]; _nd := _dtbl[1][4][4]; _nv := _dtbl[1][4][16]; if not type(_xout, 'numeric') then if member(_xout, ["start", "left", "right"]) then if _Env_smart_dsolve_numeric = true or _dtbl[1][4][10] = 1 then if _xout = "left" then if type(_dtbl[2], 'table') then return _dtbl[2][5][1] end if elif _xout = "right" then if type(_dtbl[3], 'table') then return _dtbl[3][5][1] end if end if end if; return _dtbl[1][5][5] elif _xout = "method" then return _dtbl[1][15] elif _xout = "storage" then return evalb(_dtbl[1][4][10] = 1) elif _xout = "leftdata" then if not type(_dtbl[2], 'array') then return NULL else return eval(_dtbl[2]) end if elif _xout = "rightdata" then if not type(_dtbl[3], 'array') then return NULL else return eval(_dtbl[3]) end if elif _xout = "enginedata" then return eval(_dtbl[1]) elif _xout = "enginereset" then _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); return NULL elif _xout = "initial" then return procname(_y0[0]) elif _xout = "laxtol" then return _dtbl[`if`(member(_dtbl[4], {2, 3}), _dtbl[4], 1)][5][18] elif _xout = "numfun" then return `if`(member(_dtbl[4], {2, 3}), _dtbl[_dtbl[4]][4][18], 0) elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return procname(_y0[0]), [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "last" then if _dtbl[4] <> 2 and _dtbl[4] <> 3 or _x0-_dtbl[_dtbl[4]][5][1] = 0. then error "no information is available on last computed point" else _xout := _dtbl[_dtbl[4]][5][1] end if elif _xout = "function" then if _dtbl[1][4][33]-2. = 0 then return eval(_dtbl[1][10], 1) else return eval(_dtbl[1][10][1], 1) end if elif _xout = "map" then return copy(_vmap) elif type(_xin, `=`) and type(rhs(_xin), 'list') and member(lhs(_xin), {"initial", "parameters", "initial_and_parameters"}) then _ini, _par := [], []; if lhs(_xin) = "initial" then _ini := rhs(_xin) elif lhs(_xin) = "parameters" then _par := rhs(_xin) elif select(type, rhs(_xin), `=`) <> [] then _par, _ini := selectremove(type, rhs(_xin), `=`) elif nops(rhs(_xin)) < nops(_pars)+1 then error "insufficient data for specification of initial and parameters" else _par := rhs(_xin)[-nops(_pars) .. -1]; _ini := rhs(_xin)[1 .. -nops(_pars)-1] end if; _xout := lhs(_xout); if _par <> [] then `dsolve/numeric/process_parameters`(_n, _pars, _par, _y0) end if; if _ini <> [] then `dsolve/numeric/process_initial`(_n-_ne, _ini, _y0, _pars, _vmap) end if; `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars); if _Env_smart_dsolve_numeric = true and type(_y0[0], 'numeric') and _dtbl[1][4][10] <> 1 then procname("right") := _y0[0]; procname("left") := _y0[0] end if; if _xout = "initial" then return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)] elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] else return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)], [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] end if elif _xin = "eventstop" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then return 0 end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 100 and 100 <= _dtbl[5-_i][4][9] then _i := 5-_i; _dtbl[4] := _i; _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) elif 100 <= _dtbl[_i][4][9] then _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) else return 0 end if elif _xin = "eventstatus" then if _nv = 0 then error "this solution has no events" end if; _i := [selectremove(proc (a) options operator, arrow; _dtbl[1][3][1][a, 7] = 1 end proc, {seq(_j, _j = 1 .. round(_dtbl[1][3][1][_nv+1, 1]))})]; return ':-enabled' = _i[1], ':-disabled' = _i[2] elif _xin = "eventclear" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then error "no events to clear" end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 100 and 100 < _dtbl[5-_i][4][9] then _dtbl[4] := 5-_i; _i := 5-_i end if; if _dtbl[_i][4][9] < 100 then error "no events to clear" elif _nv < _dtbl[_i][4][9]-100 then error "event error condition cannot be cleared" else _j := _dtbl[_i][4][9]-100; if irem(round(_dtbl[_i][3][1][_j, 4]), 2) = 1 then error "retriggerable events cannot be cleared" end if; _j := round(_dtbl[_i][3][1][_j, 1]); for _k to _nv do if _dtbl[_i][3][1][_k, 1] = _j then if _dtbl[_i][3][1][_k, 2] = 3 then error "range events cannot be cleared" end if; _dtbl[_i][3][1][_k, 8] := _dtbl[_i][3][1][_nv+1, 8] end if end do; _dtbl[_i][4][17] := 0; _dtbl[_i][4][9] := 0; if _dtbl[1][4][10] = 1 then if _i = 2 then try procname(procname("left")) catch: end try else try procname(procname("right")) catch: end try end if end if end if; return elif type(_xin, `=`) and member(lhs(_xin), {"eventdisable", "eventenable"}) then if _nv = 0 then error "this solution has no events" end if; if type(rhs(_xin), {('list')('posint'), ('set')('posint')}) then _i := {op(rhs(_xin))} elif type(rhs(_xin), 'posint') then _i := {rhs(_xin)} else error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; if select(proc (a) options operator, arrow; _nv < a end proc, _i) <> {} then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _k := {}; for _j to _nv do if member(round(_dtbl[1][3][1][_j, 1]), _i) then _k := `union`(_k, {_j}) end if end do; _i := _k; if lhs(_xin) = "eventdisable" then _dtbl[4] := 0; _j := [evalb(assigned(_dtbl[2]) and member(_dtbl[2][4][17], _i)), evalb(assigned(_dtbl[3]) and member(_dtbl[3][4][17], _i))]; for _k in _i do _dtbl[1][3][1][_k, 7] := 0; if assigned(_dtbl[2]) then _dtbl[2][3][1][_k, 7] := 0 end if; if assigned(_dtbl[3]) then _dtbl[3][3][1][_k, 7] := 0 end if end do; if _j[1] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[2][3][4][_k, 1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to defined init `, _dtbl[2][3][4][_k, 1]); _dtbl[2][3][1][_k, 8] := _dtbl[2][3][4][_k, 1] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to rate hysteresis init `, _dtbl[2][5][24]); _dtbl[2][3][1][_k, 8] := _dtbl[2][5][24] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to initial init `, _x0); _dtbl[2][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to fireinitial init `, _x0-1); _dtbl[2][3][1][_k, 8] := _x0-1 end if end do; _dtbl[2][4][17] := 0; _dtbl[2][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("left")) end if end if; if _j[2] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[3][3][4][_k, 2], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to defined init `, _dtbl[3][3][4][_k, 2]); _dtbl[3][3][1][_k, 8] := _dtbl[3][3][4][_k, 2] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to rate hysteresis init `, _dtbl[3][5][24]); _dtbl[3][3][1][_k, 8] := _dtbl[3][5][24] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to initial init `, _x0); _dtbl[3][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to fireinitial init `, _x0+1); _dtbl[3][3][1][_k, 8] := _x0+1 end if end do; _dtbl[3][4][17] := 0; _dtbl[3][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("right")) end if end if else for _k in _i do _dtbl[1][3][1][_k, 7] := 1 end do; _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); _dtbl[4] := 0; if _dtbl[1][4][10] = 1 then if _x0 <= procname("right") then try procname(procname("right")) catch: end try end if; if procname("left") <= _x0 then try procname(procname("left")) catch: end try end if end if end if; return elif type(_xin, `=`) and lhs(_xin) = "eventfired" then if not type(rhs(_xin), 'list') then error "'eventfired' must be specified as a list" end if; if _nv = 0 then error "this solution has no events" end if; if _dtbl[4] <> 2 and _dtbl[4] <> 3 then error "'direction' must be set prior to calling/setting 'eventfired'" end if; _i := _dtbl[4]; _val := NULL; if not assigned(_EnvEventRetriggerWarned) then _EnvEventRetriggerWarned := false end if; for _k in rhs(_xin) do if type(_k, 'integer') then _src := _k elif type(_k, 'integer' = 'anything') and type(evalf(rhs(_k)), 'numeric') then _k := lhs(_k) = evalf[max(Digits, 18)](rhs(_k)); _src := lhs(_k) else error "'eventfired' entry is not valid: %1", _k end if; if _src < 1 or round(_dtbl[1][3][1][_nv+1, 1]) < _src then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _src := {seq(`if`(_dtbl[1][3][1][_j, 1]-_src = 0., _j, NULL), _j = 1 .. _nv)}; if nops(_src) <> 1 then error "'eventfired' can only be set/queried for root-finding events and time/interval events" end if; _src := _src[1]; if _dtbl[1][3][1][_src, 2] <> 0. and _dtbl[1][3][1][_src, 2]-2. <> 0. then error "'eventfired' can only be set/queried for root-finding events and time/interval events" elif irem(round(_dtbl[1][3][1][_src, 4]), 2) = 1 then if _EnvEventRetriggerWarned = false then WARNING(`'eventfired' has no effect on events that retrigger`) end if; _EnvEventRetriggerWarned := true end if; if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then _val := _val, undefined elif type(_dtbl[_i][3][4][_src, _i-1], 'undefined') or _i = 2 and _dtbl[2][3][1][_src, 8] < _dtbl[2][3][4][_src, 1] or _i = 3 and _dtbl[3][3][4][_src, 2] < _dtbl[3][3][1][_src, 8] then _val := _val, _dtbl[_i][3][1][_src, 8] else _val := _val, _dtbl[_i][3][4][_src, _i-1] end if; if type(_k, `=`) then if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then error "cannot set event code for a rate hysteresis event" end if; userinfo(3, {'events', 'eventreset'}, `manual set event code `, _src, ` to value `, rhs(_k)); _dtbl[_i][3][1][_src, 8] := rhs(_k); _dtbl[_i][3][4][_src, _i-1] := rhs(_k) end if end do; return [_val] elif type(_xin, `=`) and lhs(_xin) = "direction" then if not member(rhs(_xin), {-1, 1, ':-left', ':-right'}) then error "'direction' must be specified as either '1' or 'right' (positive) or '-1' or 'left' (negative)" end if; _src := `if`(_dtbl[4] = 2, -1, `if`(_dtbl[4] = 3, 1, undefined)); _i := `if`(member(rhs(_xin), {1, ':-right'}), 3, 2); _dtbl[4] := _i; _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if; return _src elif _xin = "eventcount" then if _dtbl[1][3][1] = 0 or _dtbl[4] <> 2 and _dtbl[4] <> 3 then return 0 else return round(_dtbl[_dtbl[4]][3][1][_nv+1, 12]) end if else return "procname" end if end if; if _xout = _x0 then return [_x0, seq(evalf(_dtbl[1][6][_vmap[_i]]), _i = 1 .. _n-_ne)] end if; _i := `if`(_x0 <= _xout, 3, 2); if _xin = "last" and 0 < _dtbl[_i][4][9] and _dtbl[_i][4][9] < 100 then _dat := eval(_dtbl[_i], 2); _j := _dat[4][20]; return [_dat[11][_j, 0], seq(_dat[11][_j, _vmap[_i]], _i = 1 .. _n-_ne-_nd), seq(_dat[8][1][_vmap[_i]], _i = _n-_ne-_nd+1 .. _n-_ne)] end if; if not type(_dtbl[_i], 'array') then _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if end if; if _xin <> "last" then if 0 < 2 then if `dsolve/numeric/checkglobals`(op(_dtbl[1][14]), _pars, _n, _y0) then `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars, _i) end if end if; if _dtbl[1][4][7] = 0 then error "parameters must be initialized before solution can be computed" end if end if; _dat := eval(_dtbl[_i], 2); _dtbl[4] := _i; try _src := `dsolve/numeric/SC/IVPrun`(_dat, _xout) catch: userinfo(2, `dsolve/debug`, print(`Exception in solnproc:`, [lastexception][2 .. -1])); error end try; if _dat[17] <> _dtbl[1][17] then _dtbl[1][17] := _dat[17]; _dtbl[1][10] := _dat[10] end if; if _src = 0 and 100 < _dat[4][9] then _val := _dat[3][1][_nv+1, 8] else _val := _dat[11][_dat[4][20], 0] end if; if _src <> 0 or _dat[4][9] <= 0 then _dtbl[1][5][1] := _xout else _dtbl[1][5][1] := _val end if; if _i = 3 and _val < _xout then Rounding := -infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further right of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further right of %1, maxfun limit exceeded (see <a href='http://www.maplesoft.com/support/help/search.aspx?term=dsolve,maxfun' target='_new'>?dsolve,maxfun</a> for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further right of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further right of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif _dat[4][9] = 6 then error "cannot evaluate the solution further right of %1, cannot downgrade delay storage for problems with delay derivative order > 1, try increasing delaypts", evalf[8](_val) elif _dat[4][9] = 10 then error "cannot evaluate the solution further right of %1, interrupt requested", evalf[8](_val) elif 100 < _dat[4][9] then if _dat[4][9]-100 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further right of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-100, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further right of %1", evalf[8](_val) end if elif _i = 2 and _xout < _val then Rounding := infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further left of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further left of %1, maxfun limit exceeded (see <a href='http://www.maplesoft.com/support/help/search.aspx?term=dsolve,maxfun' target='_new'>?dsolve,maxfun</a> for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further left of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further left of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif _dat[4][9] = 6 then error "cannot evaluate the solution further left of %1, cannot downgrade delay storage for problems with delay derivative order > 1, try increasing delaypts", evalf[8](_val) elif _dat[4][9] = 10 then error "cannot evaluate the solution further right of %1, interrupt requested", evalf[8](_val) elif 100 < _dat[4][9] then if _dat[4][9]-100 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further left of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-100, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further left of %1", evalf[8](_val) end if end if; if _EnvInFsolve = true then _dig := _dat[4][26]; if type(_EnvDSNumericSaveDigits, 'posint') then _dat[4][26] := _EnvDSNumericSaveDigits else _dat[4][26] := Digits end if; _Env_dsolve_SC_native := true; if _dat[4][25] = 1 then _i := 1; _dat[4][25] := 2 else _i := _dat[4][25] end if; _val := `dsolve/numeric/SC/IVPval`(_dat, _xout, _src); _dat[4][25] := _i; _dat[4][26] := _dig; [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] else Digits := _dat[4][26]; _val := `dsolve/numeric/SC/IVPval`(eval(_dat, 2), _xout, _src); [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] end if end proc, (2) = Array(1..2, {(1) = 18446745843388771334, (2) = 18446745843388771510}), (3) = [t, h(t)], (4) = [ATank = ATank, pBegin = pBegin]}); _solnproc := _dat[1]; _pars := map(rhs, _dat[4]); if not type(_xout, 'numeric') then if member(t, ["start", 'start', "method", 'method', "left", 'left', "right", 'right', "leftdata", "rightdata", "enginedata", "eventstop", 'eventstop', "eventclear", 'eventclear', "eventstatus", 'eventstatus', "eventcount", 'eventcount', "laxtol", 'laxtol', "numfun", 'numfun', NULL]) then _res := _solnproc(convert(t, 'string')); if 1 < nops([_res]) then return _res elif type(_res, 'array') then return eval(_res, 1) elif _res <> "procname" then return _res end if elif member(t, ["last", 'last', "initial", 'initial', NULL]) then _res := _solnproc(convert(t, 'string')); if type(_res, 'list') then return _res[2] else return NULL end if elif member(t, ["parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(t, 'string'); _res := _solnproc(_xout); if _xout = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [_res[2], seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] end if elif type(_xout, `=`) and member(lhs(_xout), ["initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(lhs(t), 'string') = rhs(t); if lhs(_xout) = "initial" then if type(rhs(_xout), 'list') then _res := _solnproc(_xout) else _res := _solnproc("initial" = ["single", 2, rhs(_xout)]) end if elif not type(rhs(_xout), 'list') then error "initial and/or parameter values must be specified in a list" elif lhs(_xout) = "initial_and_parameters" and nops(rhs(_xout)) = nops(_pars)+1 then _res := _solnproc(lhs(_xout) = ["single", 2, op(rhs(_xout))]) else _res := _solnproc(_xout) end if; if lhs(_xout) = "initial" then return _res[2] elif lhs(_xout) = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [_res[2], seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] end if elif type(_xout, `=`) and member(lhs(_xout), ["eventdisable", 'eventdisable', "eventenable", 'eventenable', "eventfired", 'eventfired', "direction", 'direction', NULL]) then return _solnproc(convert(lhs(t), 'string') = rhs(t)) elif _xout = "solnprocedure" then return eval(_solnproc) elif _xout = "sysvars" then return _dat[3] end if; if procname <> unknown then return ('procname')(t) else _ndsol := 1; _ndsol := `tools/gensym`("h(t)"); eval(FromInert(_Inert_FUNCTION(_Inert_NAME("assign"), _Inert_EXPSEQ(ToInert(_ndsol), _Inert_VERBATIM(pointto(_dat[2][2])))))); return FromInert(_Inert_FUNCTION(ToInert(_ndsol), _Inert_EXPSEQ(ToInert(t)))) end if end if; try _res := _solnproc(_xout); _res[2] catch: error end try end proc]

(4.2)
> 

h := rhs(sol[2])

proc (t) local _res, _dat, _solnproc, _xout, _ndsol, _pars, _i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; if 1 < nargs then error "invalid input: too many arguments" end if; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then _xout := evalf[_EnvDSNumericSaveDigits](t) else _xout := evalf(t) end if; _dat := Array(1..4, {(1) = proc (_xin) local _xout, _dtbl, _dat, _vmap, _x0, _y0, _val, _dig, _n, _ne, _nd, _nv, _pars, _ini, _par, _i, _j, _k, _src; option `Copyright (c) 2002 by Waterloo Maple Inc. All rights reserved.`; table( [( "complex" ) = false ] ) _xout := _xin; _pars := [ATank = ATank, pBegin = pBegin]; _dtbl := array( 1 .. 4, [( 1 ) = (array( 1 .. 26, [( 1 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 2 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 3 ) = ([0, 0, 0, Array(1..0, 1..2, {}, datatype = float[8], order = C_order)]), ( 4 ) = (Array(1..63, {(1) = 1, (2) = 1, (3) = 0, (4) = 0, (5) = 2, (6) = 0, (7) = 0, (8) = 0, (9) = 0, (10) = 0, (11) = 0, (12) = 0, (13) = 0, (14) = 0, (15) = 0, (16) = 0, (17) = 0, (18) = 0, (19) = 30000, (20) = 0, (21) = 0, (22) = 1, (23) = 4, (24) = 0, (25) = 1, (26) = 15, (27) = 1, (28) = 0, (29) = 1, (30) = 3, (31) = 3, (32) = 0, (33) = 1, (34) = 0, (35) = 0, (36) = 0, (37) = 0, (38) = 0, (39) = 0, (40) = 0, (41) = 0, (42) = 0, (43) = 1, (44) = 0, (45) = 0, (46) = 0, (47) = 0, (48) = 0, (49) = 0, (50) = 50, (51) = 1, (52) = 0, (53) = 0, (54) = 0, (55) = 0, (56) = 0, (57) = 0, (58) = 0, (59) = 10000, (60) = 0, (61) = 1000, (62) = 0, (63) = 0}, datatype = integer[8])), ( 5 ) = (Array(1..28, {(1) = .0, (2) = 0.10e-5, (3) = .0, (4) = 0.500001e-14, (5) = .0, (6) = .0, (7) = .0, (8) = 0.10e-5, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = 1.0, (14) = .0, (15) = .49999999999999, (16) = .0, (17) = 1.0, (18) = 1.0, (19) = .0, (20) = .0, (21) = 1.0, (22) = 1.0, (23) = .0, (24) = .0, (25) = 0.10e-14, (26) = .0, (27) = .0, (28) = .0}, datatype = float[8], order = C_order)), ( 6 ) = (Array(1..3, {(1) = 0.1753773477e-1, (2) = Float(undefined), (3) = Float(undefined)})), ( 7 ) = ([Array(1..4, 1..7, {(1, 1) = .0, (1, 2) = .203125, (1, 3) = .3046875, (1, 4) = .75, (1, 5) = .8125, (1, 6) = .40625, (1, 7) = .8125, (2, 1) = 0.6378173828125e-1, (2, 2) = .0, (2, 3) = .279296875, (2, 4) = .27237892150878906, (2, 5) = -0.9686851501464844e-1, (2, 6) = 0.1956939697265625e-1, (2, 7) = .5381584167480469, (3, 1) = 0.31890869140625e-1, (3, 2) = .0, (3, 3) = -.34375, (3, 4) = -.335235595703125, (3, 5) = .2296142578125, (3, 6) = .41748046875, (3, 7) = 11.480712890625, (4, 1) = 0.9710520505905151e-1, (4, 2) = .0, (4, 3) = .40350341796875, (4, 4) = 0.20297467708587646e-1, (4, 5) = -0.6054282188415527e-2, (4, 6) = -0.4770040512084961e-1, (4, 7) = .77858567237854}, datatype = float[8], order = C_order), Array(1..6, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = 1.0, (2, 1) = .25, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = 1.0, (3, 1) = .1875, (3, 2) = .5625, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = 2.0, (4, 1) = .23583984375, (4, 2) = -.87890625, (4, 3) = .890625, (4, 4) = .0, (4, 5) = .0, (4, 6) = .2681884765625, (5, 1) = .1272735595703125, (5, 2) = -.5009765625, (5, 3) = .44921875, (5, 4) = -0.128936767578125e-1, (5, 5) = .0, (5, 6) = 0.626220703125e-1, (6, 1) = -0.927734375e-1, (6, 2) = .626220703125, (6, 3) = -.4326171875, (6, 4) = .1418304443359375, (6, 5) = -0.861053466796875e-1, (6, 6) = .3131103515625}, datatype = float[8], order = C_order), Array(1..6, {(1) = .0, (2) = .386, (3) = .21, (4) = .63, (5) = 1.0, (6) = 1.0}, datatype = float[8], order = C_order), Array(1..6, {(1) = .25, (2) = -.1043, (3) = .1035, (4) = -0.362e-1, (5) = .0, (6) = .0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 1.544, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = .9466785280815533, (3, 2) = .25570116989825814, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = 3.3148251870684886, (4, 2) = 2.896124015972123, (4, 3) = .9986419139977808, (4, 4) = .0, (4, 5) = .0, (5, 1) = 1.2212245092262748, (5, 2) = 6.019134481287752, (5, 3) = 12.537083329320874, (5, 4) = -.687886036105895, (5, 5) = .0, (6, 1) = 1.2212245092262748, (6, 2) = 6.019134481287752, (6, 3) = 12.537083329320874, (6, 4) = -.687886036105895, (6, 5) = 1.0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = -5.6688, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = -2.4300933568337584, (3, 2) = -.20635991570891224, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = -.10735290581452621, (4, 2) = -9.594562251021896, (4, 3) = -20.470286148096154, (4, 4) = .0, (4, 5) = .0, (5, 1) = 7.496443313968615, (5, 2) = -10.246804314641219, (5, 3) = -33.99990352819906, (5, 4) = 11.708908932061595, (5, 5) = .0, (6, 1) = 8.083246795922411, (6, 2) = -7.981132988062785, (6, 3) = -31.52159432874373, (6, 4) = 16.319305431231363, (6, 5) = -6.0588182388340535}, datatype = float[8], order = C_order), Array(1..3, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 10.126235083446911, (2, 2) = -7.487995877607633, (2, 3) = -34.800918615557414, (2, 4) = -7.9927717075687275, (2, 5) = 1.0251377232956207, (3, 1) = -.6762803392806898, (3, 2) = 6.087714651678606, (3, 3) = 16.43084320892463, (3, 4) = 24.767225114183653, (3, 5) = -6.5943891257167815}, datatype = float[8], order = C_order)]), ( 9 ) = ([Array(1..1, {(1) = .1}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..1, {(1, 1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..1, {(1, 1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..1, {(1, 1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = 0}, datatype = integer[8]), Array(1..3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8], order = C_order), Array(1..3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8], order = C_order), Array(1..3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8], order = C_order), Array(1..3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..2, {(1) = .0, (2) = .0}, datatype = float[8], order = C_order)]), ( 8 ) = ([Array(1..3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8], order = C_order), Array(1..3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), 0, 0]), ( 11 ) = (Array(1..6, 0..1, {(1, 1) = .0, (2, 0) = .0, (2, 1) = .0, (3, 0) = .0, (3, 1) = .0, (4, 0) = .0, (4, 1) = .0, (5, 0) = .0, (5, 1) = .0, (6, 0) = .0, (6, 1) = .0}, datatype = float[8], order = C_order)), ( 10 ) = ([proc (N, X, Y, YP) option `[Y[1] = h(t)]`; if (8552986001.*Y[1]-600000000.)*(0.8390479267e18*Y[1]^2-0.8751250239e19*Y[1]-0.4513540622e13*Y[3]+0.6097793382e18) < 0 then YP[1] := undefined; return 0 end if; YP[1] := 0.14049629468405215647e-9*evalf(((8552986001.*Y[1]-600000000.)*(0.8390479267e18*Y[1]^2-0.8751250239e19*Y[1]-0.4513540622e13*Y[3]+0.6097793382e18))^(1/2))/((8552986001.*Y[1]-600000000.)*Y[2]); 0 end proc, -1, 0, 0, 0, 0, 0, 0]), ( 13 ) = (), ( 12 ) = (), ( 15 ) = ("rkf45"), ( 14 ) = ([2, table( [( 2, "local" ) = pBegin, ( 2, "name" ) = pBegin, ( 1, "value" ) = undefined, ( 1, "local" ) = ATank, ( 1, "name" ) = ATank, ( 2, "value" ) = undefined ] )]), ( 18 ) = ([]), ( 19 ) = (0), ( 16 ) = ([0, 0, 0, []]), ( 17 ) = ([proc (N, X, Y, YP) option `[Y[1] = h(t)]`; if (8552986001.*Y[1]-600000000.)*(0.8390479267e18*Y[1]^2-0.8751250239e19*Y[1]-0.4513540622e13*Y[3]+0.6097793382e18) < 0 then YP[1] := undefined; return 0 end if; YP[1] := 0.14049629468405215647e-9*evalf(((8552986001.*Y[1]-600000000.)*(0.8390479267e18*Y[1]^2-0.8751250239e19*Y[1]-0.4513540622e13*Y[3]+0.6097793382e18))^(1/2))/((8552986001.*Y[1]-600000000.)*Y[2]); 0 end proc, -1, 0, 0, 0, 0, 0, 0]), ( 22 ) = (0), ( 23 ) = (0), ( 20 ) = ([]), ( 21 ) = (0), ( 26 ) = (Array(1..0, {})), ( 25 ) = (Array(1..0, {})), ( 24 ) = (0) ] )) ] ); _y0 := Array(0..3, {(1) = 0., (2) = 0.1753773477e-1, (3) = undefined}); _vmap := array( 1 .. 1, [( 1 ) = (1) ] ); _x0 := _dtbl[1][5][5]; _n := _dtbl[1][4][1]; _ne := _dtbl[1][4][3]; _nd := _dtbl[1][4][4]; _nv := _dtbl[1][4][16]; if not type(_xout, 'numeric') then if member(_xout, ["start", "left", "right"]) then if _Env_smart_dsolve_numeric = true or _dtbl[1][4][10] = 1 then if _xout = "left" then if type(_dtbl[2], 'table') then return _dtbl[2][5][1] end if elif _xout = "right" then if type(_dtbl[3], 'table') then return _dtbl[3][5][1] end if end if end if; return _dtbl[1][5][5] elif _xout = "method" then return _dtbl[1][15] elif _xout = "storage" then return evalb(_dtbl[1][4][10] = 1) elif _xout = "leftdata" then if not type(_dtbl[2], 'array') then return NULL else return eval(_dtbl[2]) end if elif _xout = "rightdata" then if not type(_dtbl[3], 'array') then return NULL else return eval(_dtbl[3]) end if elif _xout = "enginedata" then return eval(_dtbl[1]) elif _xout = "enginereset" then _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); return NULL elif _xout = "initial" then return procname(_y0[0]) elif _xout = "laxtol" then return _dtbl[`if`(member(_dtbl[4], {2, 3}), _dtbl[4], 1)][5][18] elif _xout = "numfun" then return `if`(member(_dtbl[4], {2, 3}), _dtbl[_dtbl[4]][4][18], 0) elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return procname(_y0[0]), [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "last" then if _dtbl[4] <> 2 and _dtbl[4] <> 3 or _x0-_dtbl[_dtbl[4]][5][1] = 0. then error "no information is available on last computed point" else _xout := _dtbl[_dtbl[4]][5][1] end if elif _xout = "function" then if _dtbl[1][4][33]-2. = 0 then return eval(_dtbl[1][10], 1) else return eval(_dtbl[1][10][1], 1) end if elif _xout = "map" then return copy(_vmap) elif type(_xin, `=`) and type(rhs(_xin), 'list') and member(lhs(_xin), {"initial", "parameters", "initial_and_parameters"}) then _ini, _par := [], []; if lhs(_xin) = "initial" then _ini := rhs(_xin) elif lhs(_xin) = "parameters" then _par := rhs(_xin) elif select(type, rhs(_xin), `=`) <> [] then _par, _ini := selectremove(type, rhs(_xin), `=`) elif nops(rhs(_xin)) < nops(_pars)+1 then error "insufficient data for specification of initial and parameters" else _par := rhs(_xin)[-nops(_pars) .. -1]; _ini := rhs(_xin)[1 .. -nops(_pars)-1] end if; _xout := lhs(_xout); if _par <> [] then `dsolve/numeric/process_parameters`(_n, _pars, _par, _y0) end if; if _ini <> [] then `dsolve/numeric/process_initial`(_n-_ne, _ini, _y0, _pars, _vmap) end if; `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars); if _Env_smart_dsolve_numeric = true and type(_y0[0], 'numeric') and _dtbl[1][4][10] <> 1 then procname("right") := _y0[0]; procname("left") := _y0[0] end if; if _xout = "initial" then return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)] elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] else return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)], [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] end if elif _xin = "eventstop" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then return 0 end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 100 and 100 <= _dtbl[5-_i][4][9] then _i := 5-_i; _dtbl[4] := _i; _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) elif 100 <= _dtbl[_i][4][9] then _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) else return 0 end if elif _xin = "eventstatus" then if _nv = 0 then error "this solution has no events" end if; _i := [selectremove(proc (a) options operator, arrow; _dtbl[1][3][1][a, 7] = 1 end proc, {seq(_j, _j = 1 .. round(_dtbl[1][3][1][_nv+1, 1]))})]; return ':-enabled' = _i[1], ':-disabled' = _i[2] elif _xin = "eventclear" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then error "no events to clear" end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 100 and 100 < _dtbl[5-_i][4][9] then _dtbl[4] := 5-_i; _i := 5-_i end if; if _dtbl[_i][4][9] < 100 then error "no events to clear" elif _nv < _dtbl[_i][4][9]-100 then error "event error condition cannot be cleared" else _j := _dtbl[_i][4][9]-100; if irem(round(_dtbl[_i][3][1][_j, 4]), 2) = 1 then error "retriggerable events cannot be cleared" end if; _j := round(_dtbl[_i][3][1][_j, 1]); for _k to _nv do if _dtbl[_i][3][1][_k, 1] = _j then if _dtbl[_i][3][1][_k, 2] = 3 then error "range events cannot be cleared" end if; _dtbl[_i][3][1][_k, 8] := _dtbl[_i][3][1][_nv+1, 8] end if end do; _dtbl[_i][4][17] := 0; _dtbl[_i][4][9] := 0; if _dtbl[1][4][10] = 1 then if _i = 2 then try procname(procname("left")) catch: end try else try procname(procname("right")) catch: end try end if end if end if; return elif type(_xin, `=`) and member(lhs(_xin), {"eventdisable", "eventenable"}) then if _nv = 0 then error "this solution has no events" end if; if type(rhs(_xin), {('list')('posint'), ('set')('posint')}) then _i := {op(rhs(_xin))} elif type(rhs(_xin), 'posint') then _i := {rhs(_xin)} else error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; if select(proc (a) options operator, arrow; _nv < a end proc, _i) <> {} then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _k := {}; for _j to _nv do if member(round(_dtbl[1][3][1][_j, 1]), _i) then _k := `union`(_k, {_j}) end if end do; _i := _k; if lhs(_xin) = "eventdisable" then _dtbl[4] := 0; _j := [evalb(assigned(_dtbl[2]) and member(_dtbl[2][4][17], _i)), evalb(assigned(_dtbl[3]) and member(_dtbl[3][4][17], _i))]; for _k in _i do _dtbl[1][3][1][_k, 7] := 0; if assigned(_dtbl[2]) then _dtbl[2][3][1][_k, 7] := 0 end if; if assigned(_dtbl[3]) then _dtbl[3][3][1][_k, 7] := 0 end if end do; if _j[1] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[2][3][4][_k, 1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to defined init `, _dtbl[2][3][4][_k, 1]); _dtbl[2][3][1][_k, 8] := _dtbl[2][3][4][_k, 1] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to rate hysteresis init `, _dtbl[2][5][24]); _dtbl[2][3][1][_k, 8] := _dtbl[2][5][24] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to initial init `, _x0); _dtbl[2][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to fireinitial init `, _x0-1); _dtbl[2][3][1][_k, 8] := _x0-1 end if end do; _dtbl[2][4][17] := 0; _dtbl[2][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("left")) end if end if; if _j[2] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[3][3][4][_k, 2], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to defined init `, _dtbl[3][3][4][_k, 2]); _dtbl[3][3][1][_k, 8] := _dtbl[3][3][4][_k, 2] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to rate hysteresis init `, _dtbl[3][5][24]); _dtbl[3][3][1][_k, 8] := _dtbl[3][5][24] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to initial init `, _x0); _dtbl[3][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to fireinitial init `, _x0+1); _dtbl[3][3][1][_k, 8] := _x0+1 end if end do; _dtbl[3][4][17] := 0; _dtbl[3][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("right")) end if end if else for _k in _i do _dtbl[1][3][1][_k, 7] := 1 end do; _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); _dtbl[4] := 0; if _dtbl[1][4][10] = 1 then if _x0 <= procname("right") then try procname(procname("right")) catch: end try end if; if procname("left") <= _x0 then try procname(procname("left")) catch: end try end if end if end if; return elif type(_xin, `=`) and lhs(_xin) = "eventfired" then if not type(rhs(_xin), 'list') then error "'eventfired' must be specified as a list" end if; if _nv = 0 then error "this solution has no events" end if; if _dtbl[4] <> 2 and _dtbl[4] <> 3 then error "'direction' must be set prior to calling/setting 'eventfired'" end if; _i := _dtbl[4]; _val := NULL; if not assigned(_EnvEventRetriggerWarned) then _EnvEventRetriggerWarned := false end if; for _k in rhs(_xin) do if type(_k, 'integer') then _src := _k elif type(_k, 'integer' = 'anything') and type(evalf(rhs(_k)), 'numeric') then _k := lhs(_k) = evalf[max(Digits, 18)](rhs(_k)); _src := lhs(_k) else error "'eventfired' entry is not valid: %1", _k end if; if _src < 1 or round(_dtbl[1][3][1][_nv+1, 1]) < _src then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _src := {seq(`if`(_dtbl[1][3][1][_j, 1]-_src = 0., _j, NULL), _j = 1 .. _nv)}; if nops(_src) <> 1 then error "'eventfired' can only be set/queried for root-finding events and time/interval events" end if; _src := _src[1]; if _dtbl[1][3][1][_src, 2] <> 0. and _dtbl[1][3][1][_src, 2]-2. <> 0. then error "'eventfired' can only be set/queried for root-finding events and time/interval events" elif irem(round(_dtbl[1][3][1][_src, 4]), 2) = 1 then if _EnvEventRetriggerWarned = false then WARNING(`'eventfired' has no effect on events that retrigger`) end if; _EnvEventRetriggerWarned := true end if; if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then _val := _val, undefined elif type(_dtbl[_i][3][4][_src, _i-1], 'undefined') or _i = 2 and _dtbl[2][3][1][_src, 8] < _dtbl[2][3][4][_src, 1] or _i = 3 and _dtbl[3][3][4][_src, 2] < _dtbl[3][3][1][_src, 8] then _val := _val, _dtbl[_i][3][1][_src, 8] else _val := _val, _dtbl[_i][3][4][_src, _i-1] end if; if type(_k, `=`) then if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then error "cannot set event code for a rate hysteresis event" end if; userinfo(3, {'events', 'eventreset'}, `manual set event code `, _src, ` to value `, rhs(_k)); _dtbl[_i][3][1][_src, 8] := rhs(_k); _dtbl[_i][3][4][_src, _i-1] := rhs(_k) end if end do; return [_val] elif type(_xin, `=`) and lhs(_xin) = "direction" then if not member(rhs(_xin), {-1, 1, ':-left', ':-right'}) then error "'direction' must be specified as either '1' or 'right' (positive) or '-1' or 'left' (negative)" end if; _src := `if`(_dtbl[4] = 2, -1, `if`(_dtbl[4] = 3, 1, undefined)); _i := `if`(member(rhs(_xin), {1, ':-right'}), 3, 2); _dtbl[4] := _i; _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if; return _src elif _xin = "eventcount" then if _dtbl[1][3][1] = 0 or _dtbl[4] <> 2 and _dtbl[4] <> 3 then return 0 else return round(_dtbl[_dtbl[4]][3][1][_nv+1, 12]) end if else return "procname" end if end if; if _xout = _x0 then return [_x0, seq(evalf(_dtbl[1][6][_vmap[_i]]), _i = 1 .. _n-_ne)] end if; _i := `if`(_x0 <= _xout, 3, 2); if _xin = "last" and 0 < _dtbl[_i][4][9] and _dtbl[_i][4][9] < 100 then _dat := eval(_dtbl[_i], 2); _j := _dat[4][20]; return [_dat[11][_j, 0], seq(_dat[11][_j, _vmap[_i]], _i = 1 .. _n-_ne-_nd), seq(_dat[8][1][_vmap[_i]], _i = _n-_ne-_nd+1 .. _n-_ne)] end if; if not type(_dtbl[_i], 'array') then _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if end if; if _xin <> "last" then if 0 < 2 then if `dsolve/numeric/checkglobals`(op(_dtbl[1][14]), _pars, _n, _y0) then `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars, _i) end if end if; if _dtbl[1][4][7] = 0 then error "parameters must be initialized before solution can be computed" end if end if; _dat := eval(_dtbl[_i], 2); _dtbl[4] := _i; try _src := `dsolve/numeric/SC/IVPrun`(_dat, _xout) catch: userinfo(2, `dsolve/debug`, print(`Exception in solnproc:`, [lastexception][2 .. -1])); error end try; if _dat[17] <> _dtbl[1][17] then _dtbl[1][17] := _dat[17]; _dtbl[1][10] := _dat[10] end if; if _src = 0 and 100 < _dat[4][9] then _val := _dat[3][1][_nv+1, 8] else _val := _dat[11][_dat[4][20], 0] end if; if _src <> 0 or _dat[4][9] <= 0 then _dtbl[1][5][1] := _xout else _dtbl[1][5][1] := _val end if; if _i = 3 and _val < _xout then Rounding := -infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further right of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further right of %1, maxfun limit exceeded (see <a href='http://www.maplesoft.com/support/help/search.aspx?term=dsolve,maxfun' target='_new'>?dsolve,maxfun</a> for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further right of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further right of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif _dat[4][9] = 6 then error "cannot evaluate the solution further right of %1, cannot downgrade delay storage for problems with delay derivative order > 1, try increasing delaypts", evalf[8](_val) elif _dat[4][9] = 10 then error "cannot evaluate the solution further right of %1, interrupt requested", evalf[8](_val) elif 100 < _dat[4][9] then if _dat[4][9]-100 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further right of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-100, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further right of %1", evalf[8](_val) end if elif _i = 2 and _xout < _val then Rounding := infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further left of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further left of %1, maxfun limit exceeded (see <a href='http://www.maplesoft.com/support/help/search.aspx?term=dsolve,maxfun' target='_new'>?dsolve,maxfun</a> for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further left of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further left of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif _dat[4][9] = 6 then error "cannot evaluate the solution further left of %1, cannot downgrade delay storage for problems with delay derivative order > 1, try increasing delaypts", evalf[8](_val) elif _dat[4][9] = 10 then error "cannot evaluate the solution further right of %1, interrupt requested", evalf[8](_val) elif 100 < _dat[4][9] then if _dat[4][9]-100 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further left of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-100, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further left of %1", evalf[8](_val) end if end if; if _EnvInFsolve = true then _dig := _dat[4][26]; if type(_EnvDSNumericSaveDigits, 'posint') then _dat[4][26] := _EnvDSNumericSaveDigits else _dat[4][26] := Digits end if; _Env_dsolve_SC_native := true; if _dat[4][25] = 1 then _i := 1; _dat[4][25] := 2 else _i := _dat[4][25] end if; _val := `dsolve/numeric/SC/IVPval`(_dat, _xout, _src); _dat[4][25] := _i; _dat[4][26] := _dig; [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] else Digits := _dat[4][26]; _val := `dsolve/numeric/SC/IVPval`(eval(_dat, 2), _xout, _src); [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] end if end proc, (2) = Array(1..2, {(1) = 18446745843388771334, (2) = 18446745843388771510}), (3) = [t, h(t)], (4) = [ATank = ATank, pBegin = pBegin]}); _solnproc := _dat[1]; _pars := map(rhs, _dat[4]); if not type(_xout, 'numeric') then if member(t, ["start", 'start', "method", 'method', "left", 'left', "right", 'right', "leftdata", "rightdata", "enginedata", "eventstop", 'eventstop', "eventclear", 'eventclear', "eventstatus", 'eventstatus', "eventcount", 'eventcount', "laxtol", 'laxtol', "numfun", 'numfun', NULL]) then _res := _solnproc(convert(t, 'string')); if 1 < nops([_res]) then return _res elif type(_res, 'array') then return eval(_res, 1) elif _res <> "procname" then return _res end if elif member(t, ["last", 'last', "initial", 'initial', NULL]) then _res := _solnproc(convert(t, 'string')); if type(_res, 'list') then return _res[2] else return NULL end if elif member(t, ["parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(t, 'string'); _res := _solnproc(_xout); if _xout = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [_res[2], seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] end if elif type(_xout, `=`) and member(lhs(_xout), ["initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(lhs(t), 'string') = rhs(t); if lhs(_xout) = "initial" then if type(rhs(_xout), 'list') then _res := _solnproc(_xout) else _res := _solnproc("initial" = ["single", 2, rhs(_xout)]) end if elif not type(rhs(_xout), 'list') then error "initial and/or parameter values must be specified in a list" elif lhs(_xout) = "initial_and_parameters" and nops(rhs(_xout)) = nops(_pars)+1 then _res := _solnproc(lhs(_xout) = ["single", 2, op(rhs(_xout))]) else _res := _solnproc(_xout) end if; if lhs(_xout) = "initial" then return _res[2] elif lhs(_xout) = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [_res[2], seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] end if elif type(_xout, `=`) and member(lhs(_xout), ["eventdisable", 'eventdisable', "eventenable", 'eventenable', "eventfired", 'eventfired', "direction", 'direction', NULL]) then return _solnproc(convert(lhs(t), 'string') = rhs(t)) elif _xout = "solnprocedure" then return eval(_solnproc) elif _xout = "sysvars" then return _dat[3] end if; if procname <> unknown then return ('procname')(t) else _ndsol := 1; _ndsol := `tools/gensym`("h(t)"); eval(FromInert(_Inert_FUNCTION(_Inert_NAME("assign"), _Inert_EXPSEQ(ToInert(_ndsol), _Inert_VERBATIM(pointto(_dat[2][2])))))); return FromInert(_Inert_FUNCTION(ToInert(_ndsol), _Inert_EXPSEQ(ToInert(t)))) end if end if; try _res := _solnproc(_xout); _res[2] catch: error end try end proc

(4.3)
> 

pBegin := 3*10^5

> 

plot(h(t), t = 0 .. 2000, labels = ['t'*[s], 'h'*[m]])

 
> 

NULL

> 

``


Hi i am trying to get a graph that shows height against time but it does not plot and I do not understand why. I copied the code of a friend and it does work on his computer. 

Download laatste_versie_berekeningen.mw

How can I animate the flattening of an octohedron?...

Asked by: Earl 985
June 17 2019
2  3

The worksheet below animates the flattening of a tetrahedron by expanding one of its faces, namely its triangular base.

I would like to animate the flattening of an octahedron so that it assumes the 2D figure resembling the Morley triangle which is included in the worksheet.

Are there documents on the web explaining the technique for doing so? Is there a Maple worksheet available on the web demonstrating the desired animation?

Flatten_a_tetrahedron.mw

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