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Question: using of Glerkin method for solving two coupled equations

Question:using of Glerkin method for solving two coupled equations

mahmood_ch 5 Maple
solve
December 06 2017
1

Hi 

I want to solve these equations in MAPLE, but something goes wrong. 


 

``

> 

restart
> 

``
> 

NULL
> 

NULL
> 

> 

> 

NULL
> 

> 

> 

phi[j] := sin(j*Pi*x)

sin(j*Pi*x)

 (1)
> 

phi[i] := sin(i*Pi*x)

sin(i*Pi*x)

 (2)
> 

phi[k] := sin(k*Pi*x)

sin(k*Pi*x)

 (3)
> 

phi[l] := sin(l*Pi*x)

sin(l*Pi*x)

 (4)
> 

phi[1] := sin(Pi*x)

sin(Pi*x)

 (5)
> 

NULL
> 

pp1 := sum((int(phi[i]*phi[j], x = 0 .. 1, numeric))*(diff(p(t), t, t))[j], j = 1 .. 8)-beta^2*(sum((int(phi[i]*(diff(phi[j], x, x)), x = 0 .. 1, numeric))*p(t)[j], j = 1 .. 8)+sum((int(AA0*(diff(phi[1], x, x))*phi[i]*(diff(phi[j], x)), x = 0 .. 1, numeric))*q[j], j = 1 .. 7)+sum((int(AA0*(diff(phi[1], x))*phi[i]*(diff(phi[j], x, x)), x = 0 .. 1, numeric))*q[j], j = 1 .. 7)+sum(sum((int(phi[i]*(diff(phi[j], x))*(diff(phi[k], x, x)), x = 0 .. 1, numeric))*q[j]*q[k], k = 1 .. 7), j = 1 .. 7))+Cd*(sum((int(phi[i]*phi[j], x = 0 .. 1, numeric))*(diff(p(t), t))[j], j = 1 .. 8)):
> 

NULL
> 

NULL
> 

NULL
> 

for z to 8 do limit(pp1, i = z) end do

limit(.1591549431*(sin(3.141592654*i-3.141592654)*i-1.*sin(3.141592654*i+3.141592654)*i+sin(3.141592654*i-3.141592654)+sin(3.141592654*i+3.141592654))*(diff(diff(p(t), t), t))[1]/((i-1.)*(i+1.))+.1591549431*(sin(3.141592654*i-6.283185308)*i-1.*sin(3.141592654*i+6.283185308)*i+2.*sin(3.141592654*i-6.283185308)+2.*sin(3.141592654*i+6.283185308))*(diff(diff(p(t), t), t))[2]/((i-2.)*(i+2.))+.1591549431*(sin(3.141592654*i-9.424777962)*i-1.*sin(3.141592654*i+9.424777962)*i+3.*sin(3.141592654*i-9.424777962)+3.*sin(3.141592654*i+9.424777962))*(diff(diff(p(t), t), t))[3]/((i-3.)*(i+3.))+.1591549431*(sin(3.141592654*i-12.56637062)*i-1.*sin(3.141592654*i+12.56637062)*i+4.*sin(3.141592654*i-12.56637062)+4.*sin(3.141592654*i+12.56637062))*(diff(diff(p(t), t), t))[4]/((i-4.)*(i+4.))+.1591549431*(sin(3.141592654*i-15.70796327)*i-1.*sin(3.141592654*i+15.70796327)*i+5.*sin(3.141592654*i-15.70796327)+5.*sin(3.141592654*i+15.70796327))*(diff(diff(p(t), t), t))[5]/((i-5.)*(i+5.))+.1591549431*(sin(3.141592654*i-18.84955592)*i-1.*sin(3.141592654*i+18.84955592)*i+6.*sin(3.141592654*i-18.84955592)+6.*sin(3.141592654*i+18.84955592))*(diff(diff(p(t), t), t))[6]/((i-6.)*(i+6.))+.1591549431*(sin(3.141592654*i-21.99114858)*i-1.*sin(3.141592654*i+21.99114858)*i+7.*sin(3.141592654*i-21.99114858)+7.*sin(3.141592654*i+21.99114858))*(diff(diff(p(t), t), t))[7]/((i-7.)*(i+7.))+.1591549431*(sin(3.141592654*i-25.13274123)*i-1.*sin(3.141592654*i+25.13274123)*i+8.*sin(3.141592654*i-25.13274123)+8.*sin(3.141592654*i+25.13274123))*(diff(diff(p(t), t), t))[8]/((i-8.)*(i+8.))-beta^2*(-1.570796327*(sin(3.141592654*i-3.141592654)*i-1.*sin(3.141592654*i+3.141592654)*i+sin(3.141592654*i-3.141592654)+sin(3.141592654*i+3.141592654))*p(t)[1]/((i-1.)*(i+1.))-6.283185308*(sin(3.141592654*i-6.283185308)*i-1.*sin(3.141592654*i+6.283185308)*i+2.*sin(3.141592654*i-6.283185308)+2.*sin(3.141592654*i+6.283185308))*p(t)[2]/((i-2.)*(i+2.))-14.13716694*(sin(3.141592654*i-9.424777962)*i-1.*sin(3.141592654*i+9.424777962)*i+3.*sin(3.141592654*i-9.424777962)+3.*sin(3.141592654*i+9.424777962))*p(t)[3]/((i-3.)*(i+3.))-25.13274123*(sin(3.141592654*i-12.56637062)*i-1.*sin(3.141592654*i+12.56637062)*i+4.*sin(3.141592654*i-12.56637062)+4.*sin(3.141592654*i+12.56637062))*p(t)[4]/((i-4.)*(i+4.))-39.26990818*(sin(3.141592654*i-15.70796327)*i-1.*sin(3.141592654*i+15.70796327)*i+5.*sin(3.141592654*i-15.70796327)+5.*sin(3.141592654*i+15.70796327))*p(t)[5]/((i-5.)*(i+5.))-56.54866777*(sin(3.141592654*i-18.84955592)*i-1.*sin(3.141592654*i+18.84955592)*i+6.*sin(3.141592654*i-18.84955592)+6.*sin(3.141592654*i+18.84955592))*p(t)[6]/((i-6.)*(i+6.))-76.96902003*(sin(3.141592654*i-21.99114858)*i-1.*sin(3.141592654*i+21.99114858)*i+7.*sin(3.141592654*i-21.99114858)+7.*sin(3.141592654*i+21.99114858))*p(t)[7]/((i-7.)*(i+7.))-100.5309649*(sin(3.141592654*i-25.13274123)*i-1.*sin(3.141592654*i+25.13274123)*i+8.*sin(3.141592654*i-25.13274123)+8.*sin(3.141592654*i+25.13274123))*p(t)[8]/((i-8.)*(i+8.))-66.61982973*(sin(3.141592654*i-18.84955592)*i^3-1.*sin(3.141592654*i+18.84955592)*i^3+6.*sin(3.141592654*i-18.84955592)*i^2+6.*sin(3.141592654*i+18.84955592)*i^2)*q[3]^2/(i^2*(i+6.)*(i-6.))-157.9136704*(-64.*sin(-0.4000000000e-8+3.141592654*i)*i+64.*sin(0.4000000000e-8+3.141592654*i)*i+sin(-0.4000000000e-8+3.141592654*i)*i^3-1.*sin(25.13274124+3.141592654*i)*i^3+sin(-25.13274124+3.141592654*i)*i^3-1.*sin(0.4000000000e-8+3.141592654*i)*i^3+8.*sin(25.13274124+3.141592654*i)*i^2+8.*sin(-25.13274124+3.141592654*i)*i^2)*q[4]^2/(i^2*(i+8.)*(i-8.))+308.4251376*(-10.*sin(31.41592654+3.141592654*i)*i^2-10.*sin(-31.41592654+3.141592654*i)*i^2+sin(31.41592654+3.141592654*i)*i^3-1.*sin(-31.41592654+3.141592654*i)*i^3)*q[5]^2/(i^2*(10.+i)*(-10.+i))-532.9586378*(144.*sin(-0.4000000000e-8+3.141592654*i)*i-144.*sin(0.4000000000e-8+3.141592654*i)*i-1.*sin(-0.4000000000e-8+3.141592654*i)*i^3+sin(0.4000000000e-8+3.141592654*i)*i^3-1.*sin(37.69911184+3.141592654*i)*i^3+sin(-37.69911184+3.141592654*i)*i^3+12.*sin(37.69911184+3.141592654*i)*i^2+12.*sin(-37.69911184+3.141592654*i)*i^2)*q[6]^2/(i^2*(12.+i)*(-12.+i))-846.3185773*(sin(-43.98229716+3.141592654*i)*i^3-1.*sin(0.2000000000e-8+3.141592654*i)*i^3+14.*sin(43.98229716+3.141592654*i)*i^2+14.*sin(-43.98229716+3.141592654*i)*i^2-196.*sin(-0.2000000000e-8+3.141592654*i)*i+196.*sin(0.2000000000e-8+3.141592654*i)*i+sin(-0.2000000000e-8+3.141592654*i)*i^3-1.*sin(43.98229716+3.141592654*i)*i^3)*q[7]^2/(i^2*(14.+i)*(-14.+i))-19.73920881*(sin(3.141592654*i-12.56637062)*i^3-1.*sin(3.141592654*i+12.56637062)*i^3+4.*sin(3.141592654*i-12.56637062)*i^2+4.*sin(3.141592654*i+12.56637062)*i^2)*q[2]^2/(i^2*(i+4.)*(i-4.))-4.934802202*AA0*(sin(3.141592654*i-6.283185308)*i-1.*sin(3.141592654*i+6.283185308)*i+2.*sin(3.141592654*i-6.283185308)+2.*sin(3.141592654*i+6.283185308))*q[1]/((i-2.)*(i+2.))-2.467401101*(sin(3.141592654*i-6.283185308)*i^3-1.*sin(3.141592654*i+6.283185308)*i^3+2.*sin(3.141592654*i-6.283185308)*i^2+2.*sin(3.141592654*i+6.283185308)*i^2)*q[1]^2/(i^2*(i+2.)*(i-2.))-9.869604403*(sin(3.141592654*i-9.424777962)*i^3-1.*sin(3.141592654*i+3.141592654)*i^3+sin(3.141592654*i-3.141592654)*i^3-1.*sin(3.141592654*i+9.424777962)*i^3+3.*sin(3.141592654*i-9.424777962)*i^2+sin(3.141592654*i+3.141592654)*i^2+sin(3.141592654*i-3.141592654)*i^2+3.*sin(3.141592654*i+9.424777962)*i^2-1.*sin(3.141592654*i-9.424777962)*i+9.*sin(3.141592654*i+3.141592654)*i-9.*sin(3.141592654*i-3.141592654)*i+sin(3.141592654*i+9.424777962)*i-3.*sin(3.141592654*i-9.424777962)-9.*sin(3.141592654*i+3.141592654)-9.*sin(3.141592654*i-3.141592654)-3.*sin(3.141592654*i+9.424777962))*q[1]*q[2]/((i-1.)*(i+3.)*(i-3.)*(i+1.))-22.20660991*(sin(3.141592654*i-12.56637062)*i^3-1.*sin(3.141592654*i+12.56637062)*i^3+sin(3.141592654*i-6.283185308)*i^3-1.*sin(3.141592654*i+6.283185308)*i^3+4.*sin(3.141592654*i-12.56637062)*i^2+4.*sin(3.141592654*i+12.56637062)*i^2+2.*sin(3.141592654*i-6.283185308)*i^2+2.*sin(3.141592654*i+6.283185308)*i^2-4.*sin(3.141592654*i-12.56637062)*i+4.*sin(3.141592654*i+12.56637062)*i-16.*sin(3.141592654*i-6.283185308)*i+16.*sin(3.141592654*i+6.283185308)*i-16.*sin(3.141592654*i-12.56637062)-16.*sin(3.141592654*i+12.56637062)-32.*sin(3.141592654*i-6.283185308)-32.*sin(3.141592654*i+6.283185308))*q[1]*q[3]/((i-2.)*(i+4.)*(i-4.)*(i+2.))-39.47841761*(-25.*sin(-9.424777966+3.141592654*i)*i+9.*sin(3.141592654*i+15.70796327)*i-9.*sin(3.141592654*i-15.70796327)*i+25.*sin(9.424777966+3.141592654*i)*i+sin(-9.424777966+3.141592654*i)*i^3-1.*sin(3.141592654*i+15.70796327)*i^3+sin(3.141592654*i-15.70796327)*i^3-1.*sin(9.424777966+3.141592654*i)*i^3+3.*sin(-9.424777966+3.141592654*i)*i^2+5.*sin(3.141592654*i+15.70796327)*i^2+5.*sin(3.141592654*i-15.70796327)*i^2+3.*sin(9.424777966+3.141592654*i)*i^2-45.*sin(3.141592654*i+15.70796327)-45.*sin(3.141592654*i-15.70796327)-75.*sin(9.424777966+3.141592654*i)-75.*sin(-9.424777966+3.141592654*i))*q[1]*q[4]/((i-3.)*(i+5.)*(i-5.)*(i+3.))+61.68502752*(-1.*sin(3.141592654*i-18.84955592)*i^3+sin(3.141592654*i+18.84955592)*i^3-6.*sin(3.141592654*i-18.84955592)*i^2-6.*sin(3.141592654*i+18.84955592)*i^2+96.*sin(3.141592654*i-18.84955592)+96.*sin(3.141592654*i+18.84955592)+16.*sin(3.141592654*i-18.84955592)*i-16.*sin(3.141592654*i+18.84955592)*i-1.*sin(3.141592654*i-12.56637062)*i^3+sin(3.141592654*i+12.56637062)*i^3-4.*sin(3.141592654*i-12.56637062)*i^2-4.*sin(3.141592654*i+12.56637062)*i^2+144.*sin(3.141592654*i+12.56637062)+144.*sin(3.141592654*i-12.56637062)+36.*sin(3.141592654*i-12.56637062)*i-36.*sin(3.141592654*i+12.56637062)*i)*q[1]*q[5]/((i-4.)*(i+6.)*(i-6.)*(i+4.))-88.82643963*(-49.*sin(3.141592654*i-15.70796327)*i+25.*sin(21.99114857+3.141592654*i)*i-25.*sin(-21.99114857+3.141592654*i)*i+49.*sin(3.141592654*i+15.70796327)*i+sin(3.141592654*i-15.70796327)*i^3-1.*sin(21.99114857+3.141592654*i)*i^3+sin(-21.99114857+3.141592654*i)*i^3-1.*sin(3.141592654*i+15.70796327)*i^3+5.*sin(3.141592654*i-15.70796327)*i^2+7.*sin(21.99114857+3.141592654*i)*i^2+7.*sin(-21.99114857+3.141592654*i)*i^2+5.*sin(3.141592654*i+15.70796327)*i^2-245.*sin(3.141592654*i-15.70796327)-175.*sin(21.99114857+3.141592654*i)-175.*sin(-21.99114857+3.141592654*i)-245.*sin(3.141592654*i+15.70796327))*q[1]*q[6]/((i-5.)*(i+7.)*(i-7.)*(i+5.))-120.9026539*(sin(3.141592654*i-25.13274123)*i^3-1.*sin(18.84955593+3.141592654*i)*i^3+6.*sin(-18.84955593+3.141592654*i)*i^2+8.*sin(3.141592654*i+25.13274123)*i^2+8.*sin(3.141592654*i-25.13274123)*i^2+6.*sin(18.84955593+3.141592654*i)*i^2-64.*sin(-18.84955593+3.141592654*i)*i+36.*sin(3.141592654*i+25.13274123)*i-36.*sin(3.141592654*i-25.13274123)*i+64.*sin(18.84955593+3.141592654*i)*i+sin(-18.84955593+3.141592654*i)*i^3-1.*sin(3.141592654*i+25.13274123)*i^3-384.*sin(18.84955593+3.141592654*i)-384.*sin(-18.84955593+3.141592654*i)-288.*sin(3.141592654*i+25.13274123)-288.*sin(3.141592654*i-25.13274123))*q[1]*q[7]/((i-6.)*(i+8.)*(i-8.)*(i+6.))-69.08723082*(-1.*sin(3.141592654*i-15.70796327)*i^3+sin(3.141592654*i+15.70796327)*i^3-5.*sin(3.141592654*i-15.70796327)*i^2-5.*sin(3.141592654*i+15.70796327)*i^2+405.*sin(3.141592654*i+15.70796327)+405.*sin(3.141592654*i-15.70796327)+81.*sin(3.141592654*i-15.70796327)*i-81.*sin(3.141592654*i+15.70796327)*i+9.*sin(28.27433389+3.141592654*i)*i^2+9.*sin(-28.27433389+3.141592654*i)*i^2+25.*sin(28.27433389+3.141592654*i)*i-25.*sin(-28.27433389+3.141592654*i)*i-1.*sin(28.27433389+3.141592654*i)*i^3+sin(-28.27433389+3.141592654*i)*i^3-225.*sin(-28.27433389+3.141592654*i)-225.*sin(28.27433389+3.141592654*i))*q[7]*q[2]/((i+5.)*(9.+i)*(-9.+i)*(i-5.))-155.4462694*(-1.*sin(3.141592654*i-12.56637062)*i^3+sin(3.141592654*i+12.56637062)*i^3-4.*sin(3.141592654*i-12.56637062)*i^2-4.*sin(3.141592654*i+12.56637062)*i^2+400.*sin(3.141592654*i+12.56637062)+400.*sin(3.141592654*i-12.56637062)+100.*sin(3.141592654*i-12.56637062)*i-100.*sin(3.141592654*i+12.56637062)*i+10.*sin(31.41592654+3.141592654*i)*i^2+10.*sin(-31.41592654+3.141592654*i)*i^2+16.*sin(31.41592654+3.141592654*i)*i-16.*sin(-31.41592654+3.141592654*i)*i-1.*sin(31.41592654+3.141592654*i)*i^3+sin(-31.41592654+3.141592654*i)*i^3-160.*sin(31.41592654+3.141592654*i)-160.*sin(-31.41592654+3.141592654*i))*q[7]*q[3]/((i+4.)*(10.+i)*(-10.+i)*(i-4.))-276.3489233*(121.*sin(-9.424777958+3.141592654*i)*i-121.*sin(9.424777958+3.141592654*i)*i-1.*sin(-9.424777958+3.141592654*i)*i^3+sin(9.424777958+3.141592654*i)*i^3-3.*sin(-9.424777958+3.141592654*i)*i^2-3.*sin(9.424777958+3.141592654*i)*i^2+9.*sin(34.55751920+3.141592654*i)*i-9.*sin(-34.55751920+3.141592654*i)*i-1.*sin(34.55751920+3.141592654*i)*i^3+sin(-34.55751920+3.141592654*i)*i^3+11.*sin(34.55751920+3.141592654*i)*i^2+11.*sin(-34.55751920+3.141592654*i)*i^2-99.*sin(34.55751920+3.141592654*i)-99.*sin(-34.55751920+3.141592654*i)+363.*sin(-9.424777958+3.141592654*i)+363.*sin(9.424777958+3.141592654*i))*q[7]*q[4]/((i+3.)*(11.+i)*(-11.+i)*(i-3.))+431.7951926*(sin(3.141592654*i-6.283185308)*i^3-1.*sin(3.141592654*i+6.283185308)*i^3+2.*sin(3.141592654*i-6.283185308)*i^2+2.*sin(3.141592654*i+6.283185308)*i^2-288.*sin(3.141592654*i+6.283185308)-288.*sin(3.141592654*i-6.283185308)+144.*sin(3.141592654*i+6.283185308)*i-144.*sin(3.141592654*i-6.283185308)*i-12.*sin(37.69911185+3.141592654*i)*i^2-12.*sin(-37.69911185+3.141592654*i)*i^2-4.*sin(37.69911185+3.141592654*i)*i+4.*sin(-37.69911185+3.141592654*i)*i+sin(37.69911185+3.141592654*i)*i^3-1.*sin(-37.69911185+3.141592654*i)*i^3+48.*sin(-37.69911185+3.141592654*i)+48.*sin(37.69911185+3.141592654*i))*q[7]*q[5]/((i+2.)*(12.+i)*(-12.+i)*(i-2.))-4.934802201*AA0*(sin(3.141592654*i-9.424777962)*i^3+sin(3.141592654*i+3.141592654)*i^3-1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^2+5.*sin(3.141592654*i+15.70796327)*i^2-81.*sin(3.141592654*i-15.70796327)*i+25.*sin(28.27433389+3.141592654*i)*i-25.*sin(-28.27433389+3.141592654*i)*i+81.*sin(3.141592654*i+15.70796327)*i+sin(3.141592654*i-15.70796327)*i^3-1.*sin(28.27433389+3.141592654*i)*i^3-225.*sin(28.27433389+3.141592654*i)-225.*sin(-28.27433389+3.141592654*i)-405.*sin(3.141592654*i+15.70796327)-405.*sin(3.141592654*i-15.70796327))*q[2]*q[7]/((i-5.)*(9.+i)*(-9.+i)*(i+5.))-7.402203303*(-1.*sin(3.141592654*i-6.283185308)*i^3+sin(3.141592654*i+6.283185308)*i^3+sin(3.141592654*i-12.56637062)*i^3-1.*sin(3.141592654*i+12.56637062)*i^3-2.*sin(3.141592654*i-6.283185308)*i^2-2.*sin(3.141592654*i+6.283185308)*i^2+4.*sin(3.141592654*i-12.56637062)*i^2+4.*sin(3.141592654*i+12.56637062)*i^2+16.*sin(3.141592654*i-6.283185308)*i-16.*sin(3.141592654*i+6.283185308)*i-4.*sin(3.141592654*i-12.56637062)*i+4.*sin(3.141592654*i+12.56637062)*i+32.*sin(3.141592654*i-6.283185308)+32.*sin(3.141592654*i+6.283185308)-16.*sin(3.141592654*i-12.56637062)-16.*sin(3.141592654*i+12.56637062))*q[3]*q[1]/((i+2.)*(i+4.)*(i-4.)*(i-2.))-29.60881321*(sin(3.141592654*i-15.70796327)*i^3-1.*sin(3.141592654*i+15.70796327)*i^3+5.*sin(3.141592654*i-15.70796327)*i^2+5.*sin(3.141592654*i+15.70796327)*i^2-5.*sin(3.141592654*i+15.70796327)-5.*sin(3.141592654*i-15.70796327)-1.*sin(3.141592654*i-15.70796327)*i+sin(3.141592654*i+15.70796327)*i+sin(3.141592654*i+3.141592654)*i^3-1.*sin(3.141592654*i-3.141592654)*i^3-1.*sin(3.141592654*i+3.141592654)*i^2-1.*sin(3.141592654*i-3.141592654)*i^2+25.*sin(3.141592654*i+3.141592654)-25.*sin(3.141592654*i+3.141592654)*i+25.*sin(3.141592654*i-3.141592654)*i+25.*sin(3.141592654*i-3.141592654))*q[3]*q[2]/((i+1.)*(i+5.)*(i-5.)*(i-1.))-118.4352528*(-49.*sin(-3.141592658+3.141592654*i)*i+sin(3.141592654*i+21.99114858)*i-1.*sin(3.141592654*i-21.99114858)*i+49.*sin(3.141592658+3.141592654*i)*i+sin(-3.141592658+3.141592654*i)*i^3-1.*sin(3.141592654*i+21.99114858)*i^3+sin(3.141592654*i-21.99114858)*i^3-1.*sin(3.141592658+3.141592654*i)*i^3+sin(-3.141592658+3.141592654*i)*i^2+7.*sin(3.141592654*i+21.99114858)*i^2+7.*sin(3.141592654*i-21.99114858)*i^2+sin(3.141592658+3.141592654*i)*i^2-7.*sin(3.141592654*i+21.99114858)-7.*sin(3.141592654*i-21.99114858)-49.*sin(3.141592658+3.141592654*i)-49.*sin(-3.141592658+3.141592654*i))*q[3]*q[4]/((i-1.)*(i+7.)*(i-7.)*(i+1.))+185.0550826*(32.*sin(3.141592654*i-25.13274123)+32.*sin(3.141592654*i+25.13274123)+4.*sin(3.141592654*i-25.13274123)*i-4.*sin(3.141592654*i+25.13274123)*i-1.*sin(3.141592654*i-6.283185308)*i^3+sin(3.141592654*i+6.283185308)*i^3-2.*sin(3.141592654*i-6.283185308)*i^2-2.*sin(3.141592654*i+6.283185308)*i^2+128.*sin(3.141592654*i+6.283185308)+128.*sin(3.141592654*i-6.283185308)-64.*sin(3.141592654*i+6.283185308)*i+64.*sin(3.141592654*i-6.283185308)*i-1.*sin(3.141592654*i-25.13274123)*i^3+sin(3.141592654*i+25.13274123)*i^3-8.*sin(3.141592654*i-25.13274123)*i^2-8.*sin(3.141592654*i+25.13274123)*i^2)*q[3]*q[5]/((i-2.)*(i+8.)*(i-8.)*(i+2.))-266.4793189*(-81.*sin(-9.424777958+3.141592654*i)*i+9.*sin(28.27433388+3.141592654*i)*i-9.*sin(-28.27433388+3.141592654*i)*i+81.*sin(9.424777958+3.141592654*i)*i+sin(-9.424777958+3.141592654*i)*i^3-1.*sin(28.27433388+3.141592654*i)*i^3+sin(-28.27433388+3.141592654*i)*i^3-1.*sin(9.424777958+3.141592654*i)*i^3+3.*sin(-9.424777958+3.141592654*i)*i^2+9.*sin(28.27433388+3.141592654*i)*i^2+9.*sin(-28.27433388+3.141592654*i)*i^2+3.*sin(9.424777958+3.141592654*i)*i^2-243.*sin(-9.424777958+3.141592654*i)-81.*sin(28.27433388+3.141592654*i)-81.*sin(-28.27433388+3.141592654*i)-243.*sin(9.424777958+3.141592654*i))*q[3]*q[6]/((i-3.)*(9.+i)*(-9.+i)*(i+3.))-362.7079617*(sin(-31.41592654+3.141592654*i)*i^3-1.*sin(3.141592654*i+12.56637062)*i^3+4.*sin(3.141592654*i-12.56637062)*i^2+10.*sin(31.41592654+3.141592654*i)*i^2+10.*sin(-31.41592654+3.141592654*i)*i^2+4.*sin(3.141592654*i+12.56637062)*i^2-100.*sin(3.141592654*i-12.56637062)*i+16.*sin(31.41592654+3.141592654*i)*i-16.*sin(-31.41592654+3.141592654*i)*i+100.*sin(3.141592654*i+12.56637062)*i+sin(3.141592654*i-12.56637062)*i^3-1.*sin(31.41592654+3.141592654*i)*i^3-160.*sin(-31.41592654+3.141592654*i)-400.*sin(3.141592654*i+12.56637062)-400.*sin(3.141592654*i-12.56637062)-160.*sin(31.41592654+3.141592654*i))*q[3]*q[7]/((i-4.)*(10.+i)*(-10.+i)*(i+4.))-9.869604404*(sin(3.141592654*i-15.70796327)*i^3-1.*sin(3.141592654*i+15.70796327)*i^3+5.*sin(3.141592654*i-15.70796327)*i^2+5.*sin(3.141592654*i+15.70796327)*i^2-45.*sin(3.141592654*i+15.70796327)-45.*sin(3.141592654*i-15.70796327)-9.*sin(3.141592654*i-15.70796327)*i+9.*sin(3.141592654*i+15.70796327)*i-1.*sin(3.141592654*i-9.424777962)*i^3+sin(3.141592654*i+9.424777962)*i^3-3.*sin(3.141592654*i-9.424777962)*i^2-3.*sin(3.141592654*i+9.424777962)*i^2+75.*sin(3.141592654*i+9.424777962)+75.*sin(3.141592654*i-9.424777962)+25.*sin(3.141592654*i-9.424777962)*i-25.*sin(3.141592654*i+9.424777962)*i)*q[4]*q[1]/((i+3.)*(i+5.)*(i-5.)*(i-3.))-39.47841761*(sin(3.141592654*i-18.84955592)*i^3-1.*sin(3.141592654*i+18.84955592)*i^3+6.*sin(3.141592654*i-18.84955592)*i^2+6.*sin(3.141592654*i+18.84955592)*i^2-24.*sin(3.141592654*i-18.84955592)-24.*sin(3.141592654*i+18.84955592)-4.*sin(3.141592654*i-18.84955592)*i+4.*sin(3.141592654*i+18.84955592)*i-1.*sin(3.141592654*i-6.283185308)*i^3+sin(3.141592654*i+6.283185308)*i^3-2.*sin(3.141592654*i-6.283185308)*i^2-2.*sin(3.141592654*i+6.283185308)*i^2+72.*sin(3.141592654*i+6.283185308)+72.*sin(3.141592654*i-6.283185308)-36.*sin(3.141592654*i+6.283185308)*i+36.*sin(3.141592654*i-6.283185308)*i)*q[4]*q[2]/((i+2.)*(i+6.)*(i-6.)*(i-2.))-88.82643964*(sin(3.141592654*i-21.99114858)*i^3-1.*sin(3.141592654*i+21.99114858)*i^3+7.*sin(3.141592654*i-21.99114858)*i^2+7.*sin(3.141592654*i+21.99114858)*i^2-7.*sin(3.141592654*i-21.99114858)-7.*sin(3.141592654*i+21.99114858)-1.*sin(3.141592654*i-21.99114858)*i+sin(3.141592654*i+21.99114858)*i+sin(3.141592654*i+3.141592654)*i^3-1.*sin(3.141592654*i-3.141592654)*i^3-1.*sin(3.141592654*i+3.141592654)*i^2-1.*sin(3.141592654*i-3.141592654)*i^2+49.*sin(3.141592654*i+3.141592654)-49.*sin(3.141592654*i+3.141592654)*i+49.*sin(3.141592654*i-3.141592654)*i+49.*sin(3.141592654*i-3.141592654))*q[4]*q[3]/((i+1.)*(i+7.)*(i-7.)*(i-1.))+246.7401101*(sin(3.141592654*i+3.141592654)*i^3-1.*sin(3.141592654*i-3.141592654)*i^3-1.*sin(3.141592654*i+3.141592654)*i^2-1.*sin(3.141592654*i-3.141592654)*i^2-9.*sin(28.27433389+3.141592654*i)*i^2-9.*sin(-28.27433389+3.141592654*i)*i^2-1.*sin(28.27433389+3.141592654*i)*i+sin(-28.27433389+3.141592654*i)*i+sin(28.27433389+3.141592654*i)*i^3-1.*sin(-28.27433389+3.141592654*i)*i^3+81.*sin(3.141592654*i+3.141592654)-81.*sin(3.141592654*i+3.141592654)*i+81.*sin(3.141592654*i-3.141592654)*i+81.*sin(3.141592654*i-3.141592654)+9.*sin(-28.27433389+3.141592654*i)+9.*sin(28.27433389+3.141592654*i))*q[4]*q[5]/((i-1.)*(9.+i)*(-9.+i)*(i+1.))-355.3057585*(-100.*sin(-6.283185304+3.141592654*i)*i+4.*sin(31.41592654+3.141592654*i)*i-4.*sin(-31.41592654+3.141592654*i)*i+100.*sin(6.283185304+3.141592654*i)*i+sin(-6.283185304+3.141592654*i)*i^3-1.*sin(31.41592654+3.141592654*i)*i^3+sin(-31.41592654+3.141592654*i)*i^3-1.*sin(6.283185304+3.141592654*i)*i^3+2.*sin(-6.283185304+3.141592654*i)*i^2+10.*sin(31.41592654+3.141592654*i)*i^2+10.*sin(-31.41592654+3.141592654*i)*i^2+2.*sin(6.283185304+3.141592654*i)*i^2-40.*sin(31.41592654+3.141592654*i)-40.*sin(-31.41592654+3.141592654*i)-200.*sin(6.283185304+3.141592654*i)-200.*sin(-6.283185304+3.141592654*i))*q[4]*q[6]/((i-2.)*(10.+i)*(-10.+i)*(i+2.))-483.6106156*(sin(-34.55751920+3.141592654*i)*i^3-1.*sin(9.424777964+3.141592654*i)*i^3+3.*sin(-9.424777964+3.141592654*i)*i^2+11.*sin(34.55751920+3.141592654*i)*i^2+11.*sin(-34.55751920+3.141592654*i)*i^2+3.*sin(9.424777964+3.141592654*i)*i^2-121.*sin(-9.424777964+3.141592654*i)*i+9.*sin(34.55751920+3.141592654*i)*i-9.*sin(-34.55751920+3.141592654*i)*i+121.*sin(9.424777964+3.141592654*i)*i+sin(-9.424777964+3.141592654*i)*i^3-1.*sin(34.55751920+3.141592654*i)*i^3-363.*sin(9.424777964+3.141592654*i)-363.*sin(-9.424777964+3.141592654*i)-99.*sin(34.55751920+3.141592654*i)-99.*sin(-34.55751920+3.141592654*i))*q[4]*q[7]/((i-3.)*(11.+i)*(-11.+i)*(i+3.)))+Cd*(.1591549431*(sin(3.141592654*i-3.141592654)*i-1.*sin(3.141592654*i+3.141592654)*i+sin(3.141592654*i-3.141592654)+sin(3.141592654*i+3.141592654))*(diff(p(t), t))[1]/((i-1.)*(i+1.))+.1591549431*(sin(3.141592654*i-6.283185308)*i-1.*sin(3.141592654*i+6.283185308)*i+2.*sin(3.141592654*i-6.283185308)+2.*sin(3.141592654*i+6.283185308))*(diff(p(t), t))[2]/((i-2.)*(i+2.))+.1591549431*(sin(3.141592654*i-9.424777962)*i-1.*sin(3.141592654*i+9.424777962)*i+3.*sin(3.141592654*i-9.424777962)+3.*sin(3.141592654*i+9.424777962))*(diff(p(t), t))[3]/((i-3.)*(i+3.))+.1591549431*(sin(3.141592654*i-12.56637062)*i-1.*sin(3.141592654*i+12.56637062)*i+4.*sin(3.141592654*i-12.56637062)+4.*sin(3.141592654*i+12.56637062))*(diff(p(t), t))[4]/((i-4.)*(i+4.))+.1591549431*(sin(3.141592654*i-15.70796327)*i-1.*sin(3.141592654*i+15.70796327)*i+5.*sin(3.141592654*i-15.70796327)+5.*sin(3.141592654*i+15.70796327))*(diff(p(t), t))[5]/((i-5.)*(i+5.))+.1591549431*(sin(3.141592654*i-18.84955592)*i-1.*sin(3.141592654*i+18.84955592)*i+6.*sin(3.141592654*i-18.84955592)+6.*sin(3.141592654*i+18.84955592))*(diff(p(t), t))[6]/((i-6.)*(i+6.))+.1591549431*(sin(3.141592654*i-21.99114858)*i-1.*sin(3.141592654*i+21.99114858)*i+7.*sin(3.141592654*i-21.99114858)+7.*sin(3.141592654*i+21.99114858))*(diff(p(t), t))[7]/((i-7.)*(i+7.))+.1591549431*(sin(3.141592654*i-25.13274123)*i-1.*sin(3.141592654*i+25.13274123)*i+8.*sin(3.141592654*i-25.13274123)+8.*sin(3.141592654*i+25.13274123))*(diff(p(t), t))[8]/((i-8.)*(i+8.))), i = 1)

  

Warning,  computation interrupted

  
> 

``
> 

``
> 

NULL
> 

pp2 := sum((int(phi[i]*phi[j], x = 0 .. 1, numeric))*(diff(q(t), t, t))[j], j = 1 .. 7)+(1+`ηη`)*(sum((int(phi[i]*(diff(phi[j], x, x, x, x)), x = 0 .. 1, numeric))*q(t)[j], j = 1 .. 7))+Cd*(sum((int(phi[i]*phi[j], x = 0 .. 1, numeric))*(diff(q(t), t))[j], j = 1 .. 7))-beta^2*(sum(sum((int(phi[i]*(diff(phi[j], x, x))*(diff(phi[k], x)), x = 0 .. 1, numeric))*q(t)[j]*p[k], k = 1 .. 8), j = 1 .. 7)+sum(sum((int(phi[i]*(diff(phi[j], x))*(diff(phi[k], x, x)), x = 0 .. 1, numeric))*q(t)[j]*p[k], k = 1 .. 8), j = 1 .. 7)+sum((int(AA0*(diff(phi[1], x, x))*phi[i]*(diff(phi[j], x)), x = 0 .. 1, numeric))*p[j], j = 1 .. 8)+sum((int(AA0*(diff(phi[1], x))*phi[i]*(diff(phi[j], x, x)), x = 0 .. 1, numeric))*p[j], j = 1 .. 8)+(3/2)*(sum(sum(sum((int(phi[i]*(diff(phi[j], x))*(diff(phi[k], x))*(diff(phi[l], x, x)), x = 0 .. 1, numeric))*q(t)[j]*q(t)[k]*q(t)[l], l = 1 .. 7), k = 1 .. 7), j = 1 .. 7))+(3/2)*(sum(sum((int(AA0*(diff(phi[1], x, x))*phi[i]*(diff(phi[j], x))*(diff(phi[k], x)), x = 0 .. 1, numeric))*q(t)[j]*q(t)[k], k = 1 .. 7), j = 1 .. 7))+sum((int((AA0*(diff(phi[1], x)))^2*phi[i]*(diff(phi[j], x, x)), x = 0 .. 1, numeric))*q(t)[j], j = 1 .. 7)+3*(sum(sum((int(AA0*(diff(phi[1], x))*phi[i]*(diff(phi[j], x))*(diff(phi[k], x, x)), x = 0 .. 1, numeric))*q(t)[j]*q(t)[k], k = 1 .. 7), j = 1 .. 7))+2*(sum((int(AA0^2*(diff(phi[1], x))*(diff(phi[1], x, x))*phi[i]*(diff(phi[j], x)), x = 0 .. 1, numeric))*q(t)[j], j = 1 .. 7)))-(int(f1*phi[1]*phi[i], x = 0 .. 1, numeric))*cos(Omega*t)
> 

NULL
> 

NULL
> 

``
> 

for z to 7 do limit(pp2, i = z) end do

Warning,  computation interrupted

  
> 

``
> 

NULL
> 

``
> 

``
> 

``
> 

``
> 

``
> 

``
> 

``
> 

``
> 

``
> 

``
> 

``
> 

``
> 

``
> 

``

``


 

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