Maple 2018 Questions and Posts

These are Posts and Questions associated with the product, Maple 2018

Hi. what is reason maple unable to integral in answer of dsolve? when I try to use dsolve for solve my equation in answer of maple there are expressions of integral that isnot calculated

∫(-625 R^2 ro (-2 cp3 x1 lambdaopt+sin((pi t)/10) cp2+(16 cp2)/5) (-cos((pi t)/10)+cos(2 pi)+((-t/5+4) x1+(8 t)/25-32/5) pi) lambdaopt pi b11 (e)^(-((16+5 sin((pi t)/10)) cp1)/(10 lambdaopt x1))+625 (-R^2 k11 (cos((pi t)/10))^3+k11 R^2 (cos(2 pi)-((t-20) (x1-8/5) pi)/5) (cos((pi t)/10))^2+((32 sin((pi t)/10) R^2 k11)/5+(281 R^2 k11)/25+4 lambdaopt^2 (a11 x1+a13 x3)) cos((pi t)/10)-(32 k11 R^2 (cos(2 pi)-((t-20) (x1-8/5) pi)/5) sin((pi t)/10))/5+(281 (x1-8/5) (R^2 k11+(100 lambdaopt^2 (a11 x1+a13 x3))/281) pi t)/125) x1^2)ⅆt

Hi,

I'm trying to solve an expression with only one unknown variable, but for some reason solve and fsolve are unable to return a solution.

The expression I'm trying to solve is:

p := k*T*m__hhw*(ln(1+exp(E__fv-E__hh0)/(k*T))+ln(1+exp(E__fv-E__hh1)/(k*T)))/(Pi*h__bar^2*L__z) = 0.3e25

where all variables are predefined and am trying to solve for E__fv. However, when I use solve, I get the error: "Warning, solutions may have been lost", and when I try to use fsolve, it simply returns the expression as an answer and I am unable to find the numerical value for E__fv. Any helps or tips are appreciated.

If it helps, the defined variable values are:

k = 1.3806E-23;

T = 300;

h__bar = 1.05456E-34

L__z = 6E-9

m__hhw = 3.862216E-31;

E__hh0 = 3.012136E-21

E__hh1 = 1.185628E-20

 

A similar expression in the previous line was able to solve correctly and return a numerical value, so I'm not sure why solve/fsolve can't solve this one.

Similar solved expression:

solve(0.3e25 = m__cw*k*T*ln(1+exp(E__fc-E__c0)/(k*T))/(Pi*h__bar^2*L__z), E__fc);
                          -42.88488490
 

I have this polynomial equation: (x-2)^2*(x-3)+epsilon =0, I want to draw a bifurcation diagram in the (epsilon , x) plane.

 

How to implement this in maple 2018?

 

Thanks!

 

Hello,
Anyone has an idea what is wrong with the following code procedure?
the result of u(x) should be a continuous function of x (and it is continuous when solved numerically)

THANKS IN ADVANCE,
Gil Soffer
 

restart;
Heaviside(0):=1:Heaviside(0.):=1:
dats:={s(x)=-Dt*(x+h/2)+st};
eqs:={diff(u(x),x)=Heaviside(sY-s(x))*s(x)/E+Heaviside(s(x)-sY)*(sY/E+(s(x)-sY)/Esec),
      u(-h/2)=y0};
sol0:=simplify(dsolve(subs(dats,eqs),u(x)));
sol1:=int(lhs(eqs[1]),x)=eval(student:-simpson(subs(x=_x,subs(dats,rhs(eqs[1]))),_x=-h/2..x,40))+y0:

dat1:={Dt=-0.1,Esec=1,E=3,sY=0.8,st=0.05,y0=5,h=10};
plot([subs(evalf(subs(dat1,sol0)),u(x)),subs(evalf(subs(dat1,sol1)),u(x))],x=-5..5,title=u(x),legend=[symbolic,numeric]);
plot(subs(subs(dat1,subs(dats,eqs[1])),diff(u(x),x)),x=-5..5,title=diff(u(x),x));


Hello guys, 

I have a probelm with computing an integral by maple. I dont know why maple cannot compute.

 

integral.mw

Thank you for your attention

Best

With this application developed entirely in Maple using native syntax and embedded components for science and engineering students. Just replace your data and you're done.

Pearson_Coeficient.mw

Lenin Araujo Castillo

Ambassador of Maple

 

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

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* (((∂)^2)/(∂r^2) f[1,1](r,theta))+7* f[1,1](r,theta)+5 *f[1,1](r,theta)-(2 *6 (((∂)^2)/(∂theta^2) f[1,1](r,theta)))/r+(0.6 (((∂)^4)/(∂r^2∂theta^2) f[1,1](r,theta)))/4+(.5 (((∂)^4)/(∂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

 

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`*(∂)/(∂r) (F*(∂)/(∂r)`u__0`(r,theta))-1/(2)*`A__0`*(∂)/(∂r) (`K__1`*`u__0`(r,theta))+1/(2)*`A__0`*`K__1`*(∂)/(∂r)`u__0`(r,theta)-1/(2)*`A__0`*(∂)/(∂ r) (`H__1`*`u__0`(r,theta))+1/(2)*`A__0`*`H__1`*(∂)/(∂r)`u__0`(r,theta)+`K__3`*`A__0`*`u__0`(r,theta)-1/(2)*`A__0`*(∂)/(∂ r) (`K__4`*`u__0`(r,theta))+1/(2)*`A__0`*`K__4`*(∂)/(∂r)`u__0`(r,theta)+`A__0`*`K__5`*`u__0`(r,theta)-2*`A__0`*(∂)/(∂ theta) ((`H__2`)/(r)*(∂)/(∂theta)`u__0`(r,theta))+(1)/(4)*`A__0`*l^(2)*((∂)^(2))/(∂ r ∂ theta)(mu*((∂)^(2))/(∂r ∂theta)`u__0`(r,theta))+(1)/(4)*`A__0`*l^(2)*((∂)^(2))/(∂theta^(2))(mu*((∂)^(2))/(∂ theta^(2))`u__0`(r,theta))+rho*`A__0`*`K__16`*((∂)^(2))/(∂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

 

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

restart;

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

 

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

 

 

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


 

e := mu*(((cosh(eta)-cos(theta))/a)^2*(diff(`U__η`(eta, `ϕ`, theta), eta, eta))+(1-cosh(eta)*cos(theta))*(cosh(eta)-cos(theta))*(diff(`U__η`(eta, `ϕ`, theta), eta))/(a^2*sinh(eta))+2*sinh(eta)*(cosh(eta)-cos(theta))*(diff(`U__θ`(eta, `ϕ`, theta), theta))/a^2)

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

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

"(∂)/(∂ A[m,n,r])L"

``

``

``

``

``

``

``

``


 

Download

 

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

Thanks.


 

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

 

 

with(plots)

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

(1)

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

 

torus

torus

(2)

``


 

Download toro.mw

 

 

\Hello,

How I can solve this algebraic to find unknowns ABCD?

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

Because I should run the code for many input data

Thanks


 

restart;

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

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

.5

 

.1

 

2700

 

0.5e-3

 

0.7240000000e11

 

.3

 

6

 

1

 

10

 

.9400000000

 

.1369508410

 

3067.173621

(1)

 

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

-0.2152568528e12

(2)

 

 

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

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

(3)

``


 

Download solve.mw

 

 

 

restart; interface(rtablesize = 10): _EnvHorizontalName := 'x': _EnvVerticalName := 'y': eqPA := (y-b0)/(x-a0) = k: solPA := y=solve(eqPA, y): #k coefficient directeur de PA eqPB := (y-b0)/(x-a0) = -1/k: solPB :=y= solve(eqPB, y):#PB perpendicalaire à PA xA := solve(subs(y = 0, eqPA), x): yB := solve(subs(x = 0, eqPB), y): eqAB := x/xA+y/yB = 1; x k y k eqAB := --------- + --------- = 1 a0 k - b0 b0 k + a0 t := solve(a*(xM+(1/2)*t*a)+b*(yM+(1/2)*t*b)+c = 0, t); 2 (a xM + b yM + c) t := - ------------------- 2 2 a + b #Recherche des coordonnées de la projection d'un point sur une droite D #M(x,y)un point quelconque du plan, M'(x',y') son symé trique dans la symétrie orthogonale d'axe D #le vecteur MM' est colinéaire du vecteur normal n de D; vec(MM')=t.vec(n), n=

Hi everybody,

Im trying to solve the following trivial pde using Maple 2018

pdsolve([diff(Y(x, t), t, t) = 0, Y(x, 0) = 0, (D[2](Y))(x, 1) = 0]);

Obviuosly the solution is Y(x, t) = 0, but Mapple 2018 is not giving any answer.

This works in Maple 2015.

Why is not working in Maple 2018?

Thanks,

Javier

 

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