torabi

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4 years, 340 days

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These are questions asked by torabi

is possible to solve this pde via maple?

m1.mwm1.mw
 

restart

sys := [-(-r^2+1)*(diff(theta(r, z), z))+(diff(theta(r, z), r)+r*(diff(theta(r, z), r, r)))/r+diff(theta(r, z), z, z)+(diff(theta(r, z), r))*(diff(sigma(r, z), r))+(diff(sigma(r, z), z))*(diff(theta(r, z), z))+(diff(theta(r, z), r))^2+(diff(theta(r, z), z))^2 = 0, -(-r^2+1)*(diff(sigma(r, z), z))+(diff(sigma(r, z), r)+r*(diff(sigma(r, z), r, r)))/r+diff(sigma(r, z), z, z)+(diff(theta(r, z), r)+r*(diff(theta(r, z), r, r)))/r+diff(theta(r, z), z, z) = 0]; IBCs := {sigma(1, z) = 1, sigma(r, 0) = 1, theta(1, z) = 1, theta(r, 0) = 1, (D[1](sigma))(0, z) = 0, (D[1](theta))(0, z) = 0, (D[2](sigma))(r, 1) = 0, (D[2](theta))(r, 1) = 0}

[-(-r^2+1)*(diff(theta(r, z), z))+(diff(theta(r, z), r)+r*(diff(diff(theta(r, z), r), r)))/r+diff(diff(theta(r, z), z), z)+(diff(theta(r, z), r))*(diff(sigma(r, z), r))+(diff(sigma(r, z), z))*(diff(theta(r, z), z))+(diff(theta(r, z), r))^2+(diff(theta(r, z), z))^2 = 0, -(-r^2+1)*(diff(sigma(r, z), z))+(diff(sigma(r, z), r)+r*(diff(diff(sigma(r, z), r), r)))/r+diff(diff(sigma(r, z), z), z)+(diff(theta(r, z), r)+r*(diff(diff(theta(r, z), r), r)))/r+diff(diff(theta(r, z), z), z) = 0]

 

{sigma(1, z) = 1, sigma(r, 0) = 1, theta(1, z) = 1, theta(r, 0) = 1, (D[1](sigma))(0, z) = 0, (D[1](theta))(0, z) = 0, (D[2](sigma))(r, 1) = 0, (D[2](theta))(r, 1) = 0}

(1)

NULL


 

Download m1.mw

 

how I can determined time period?

thank you

period.mw
 

d := (10+20*cos(Omega*t)+30*cos(9*sqrt(2)*t))^2

(10+20*cos(Omega*t)+30*cos(9*2^(1/2)*t))^2

(1)

with(StringTools)

period(d)

period((10+20*cos(Omega*t)+30*cos(9*2^(1/2)*t))^2)

(2)

``


 

Download period.mw

 

i want to gain diff(p(t), t) and diff(q(t), t) and Jacobian matrix
 according to the attached pdf file.

please help me.

thanks

simplify.mw
 

k := diff(a(t), t) = -mu*a(t)-(1/4)*alpha6*a(t)*sin(gamma(t))

diff(a(t), t) = -mu*a(t)-(1/4)*alpha6*a(t)*sin(gamma(t))

(1)

j := a(t)*(diff(gamma(t), t)) = 2*a(t)*sigma-(6*(1/8))*(alpha1-alpha2+(1/3)*alpha3)*a(t)^3-(1/2)*alpha6*a(t)*cos(gamma(t))

a(t)*(diff(gamma(t), t)) = 2*a(t)*sigma-(3/4)*(alpha1-alpha2+(1/3)*alpha3)*a(t)^3-(1/2)*alpha6*a(t)*cos(gamma(t))

(2)

"p(t):=a(t)*cos(gamma(t))"

proc (t) options operator, arrow, function_assign; a(t)*cos(gamma(t)) end proc

(3)

"q(t):=a(t)*sin(gamma(t))"

proc (t) options operator, arrow, function_assign; a(t)*sin(gamma(t)) end proc

(4)

diff(p(t), t)

(diff(a(t), t))*cos(gamma(t))-a(t)*(diff(gamma(t), t))*sin(gamma(t))

(5)

(-mu*a(t)-(1/4)*alpha6*a(t)*sin(gamma(t)))*cos(gamma(t))-a(t)*(2*sigma-(6*(1/8))*(alpha1-alpha2+(1/3)*alpha3)*a(t)^2-(1/2)*alpha6*cos(gamma(t)))*sin(gamma(t))

(-mu*a(t)-(1/4)*alpha6*a(t)*sin(gamma(t)))*cos(gamma(t))-a(t)*(2*sigma-(3/4)*(alpha1-alpha2+(1/3)*alpha3)*a(t)^2-(1/2)*alpha6*cos(gamma(t)))*sin(gamma(t))

(6)

diff(p(t), t)

2*t

(7)

``


subs.pdf

Download simplify.mw

 

 

how i can remove root of from result.

I want to plot function.

Thnaks

root_of.mw
 

sigma2 := RootOf(43980465111040000000000000000*sqrt(3)*Pi^25*sqrt(32*Pi^2+2)*sigma+21990232555520000000000000000*sqrt(3)*Pi^23*sqrt(32*Pi^2+2)*sigma-98268851732480000000000000000*sqrt(3)*Pi^21*sqrt(32*Pi^2+2)*sigma-44495861186560000000000000000*sqrt(3)*Pi^19*sqrt(32*Pi^2+2)*sigma+82188225740800000000000000000*sqrt(3)*Pi^17*sqrt(32*Pi^2+2)*sigma+33095407370240000000000000000*sqrt(3)*Pi^15*sqrt(32*Pi^2+2)*sigma-30136000839680000000000000000*sqrt(3)*Pi^13*sqrt(32*Pi^2+2)*sigma-10618895073280000000000000000*sqrt(3)*Pi^11*sqrt(32*Pi^2+2)*sigma+3822293002240000000000000000*sqrt(3)*Pi^9*sqrt(32*Pi^2+2)*sigma+1210118016000000000000000000*sqrt(3)*Pi^7*sqrt(32*Pi^2+2)*sigma+118805400000000000000000000*sqrt(3)*Pi^5*sqrt(32*Pi^2+2)*sigma+5028750000000000000000000*sqrt(3)*Pi^3*sqrt(32*Pi^2+2)*sigma+79101562500000000000000*sqrt(3)*sigma*Pi*sqrt(32*Pi^2+2)+111484894360500000*Pi^2*20^RootOf8+1765920726670320000*Pi^4*20^RootOf8-569534208772147200*Pi^6*20^RootOf8-4505569481375428608*Pi^8*20^RootOf8+972005049637797888*Pi^10*20^RootOf8+5143616921914048512*Pi^12*20^RootOf8-554194415829123072*Pi^14*20^RootOf8-2216777663316492288*Pi^16*20^RootOf8+(-9231519020818020433920000000000*Pi^22+195541371952408496701440000000000*Pi^20+89300299589267320995840000000000*Pi^18-333503605675043554590720000000000*Pi^16-115500365322956203622400000000000*Pi^14+204706142659640339988480000000000*Pi^12+55783620627641021399040000000000*Pi^10-43454880575740151285760000000000*Pi^8-9286786763553830541120000000000*Pi^6-635208422610519981000000000000*Pi^4-16054449064166199375000000000*Pi^2-85686765999732421875000000)*_Z+(1683627180032000000000000000000*Pi^28+947040288768000000000000000000*Pi^26-243897798836910985052160000000000*Pi^24-105849518880314282213376000000000*Pi^22+543806205557386676011008000000000*Pi^20+206745517628405562998784000000000*Pi^18-493535946568048375234560000000000*Pi^16-161556685841710476165120000000000*Pi^14+209521703041307302907904000000000*Pi^12+57932333046211895115008000000000*Pi^10-32606166808014116503296000000000*Pi^8-7574931806403147431400000000000*Pi^6-916854325001083153125000000000*Pi^4-60848666758777034179687500000*Pi^2-1531121744500488281250000000)*_Z^2+(14538675656595603456000000000000*Pi^20+6360670599760576512000000000000*Pi^18-24363640065154351104000000000000*Pi^16-9459367828326973440000000000000*Pi^14+10040437028153917440000000000000*Pi^12+3693930616897744896000000000000*Pi^10+1609933205706216192000000000000*Pi^8+58674582771546096000000000000*Pi^6-1202653471578517170000000000000*Pi^4-149668239567146343750000000000*Pi^2-4663745768352832031250000000)*_Z^3+(-8723205391669003498291200000000*Pi^24-4361602695834501749145600000000*Pi^22+19490912047010429691494400000000*Pi^20+8825430454852624633036800000000*Pi^18-16301436833461042151424000000000*Pi^16-6564233354119088386867200000000*Pi^14+5977256592087501137510400000000*Pi^12+2106180608207148770918400000000*Pi^10-758124018049754123827200000000*Pi^8-240018107472837924480000000000*Pi^6-23564187036740637000000000000*Pi^4-997415989180706250000000000*Pi^2-15689219628471679687500000)*_Z^4-13647882752248245117187500000-261292721157421875*20^RootOf8-535230827832343213125000000000*Pi^2-90526382422649463214540800000000*Pi^8-18587959930253464168320000000000*Pi^6-5863377073505044924800000000000*Pi^4+305811336261213249011712000000000*Pi^12+79115470702645314657484800000000*Pi^10-239241111641945951698944000000000*Pi^16-79895480796476508576153600000000*Pi^14+7986315188014109687808000000000*Pi^22-60346149989113268482867200000000*Pi^20-18258684357505568263372800000000*Pi^18+14855623787650488886886400000000*Pi^24)

F := plot([sigma2], sigma = -10 .. 10, color = [RED], thickness = 1)

Warning, expecting only range variable sigma in expression RootOf(-2216777663316492288*Pi^16*20^RootOf8-554194415829123072*Pi^14*20^RootOf8+5143616921914048512*Pi^12*20^RootOf8+33095407370240000000000000000*3^(1/2)*Pi^15*(32*Pi^2+2)^(1/2)*sigma-30136000839680000000000000000*3^(1/2)*Pi^13*(32*Pi^2+2)^(1/2)*sigma+5028750000000000000000000*3^(1/2)*Pi^3*(32*Pi^2+2)^(1/2)*sigma+79101562500000000000000*3^(1/2)*sigma*Pi*(32*Pi^2+2)^(1/2)-10618895073280000000000000000*3^(1/2)*Pi^11*(32*Pi^2+2)^(1/2)*sigma+3822293002240000000000000000*3^(1/2)*Pi^9*(32*Pi^2+2)^(1/2)*sigma+1210118016000000000000000000*3^(1/2)*Pi^7*(32*Pi^2+2)^(1/2)*sigma+118805400000000000000000000*3^(1/2)*Pi^5*(32*Pi^2+2)^(1/2)*sigma+43980465111040000000000000000*3^(1/2)*Pi^25*(32*Pi^2+2)^(1/2)*sigma+21990232555520000000000000000*3^(1/2)*Pi^23*(32*Pi^2+2)^(1/2)*sigma-98268851732480000000000000000*3^(1/2)*Pi^21*(32*Pi^2+2)^(1/2)*sigma-44495861186560000000000000000*3^(1/2)*Pi^19*(32*Pi^2+2)^(1/2)*sigma+82188225740800000000000000000*3^(1/2)*Pi^17*(32*Pi^2+2)^(1/2)*sigma+14855623787650488886886400000000*Pi^24-18587959930253464168320000000000*Pi^6-5863377073505044924800000000000*Pi^4+79115470702645314657484800000000*Pi^10-90526382422649463214540800000000*Pi^8-239241111641945951698944000000000*Pi^16-79895480796476508576153600000000*Pi^14+305811336261213249011712000000000*Pi^12-60346149989113268482867200000000*Pi^20-18258684357505568263372800000000*Pi^18+7986315188014109687808000000000*Pi^22-535230827832343213125000000000*Pi^2+111484894360500000*Pi^2*20^RootOf8+1765920726670320000*Pi^4*20^RootOf8-569534208772147200*Pi^6*20^RootOf8-4505569481375428608*Pi^8*20^RootOf8+972005049637797888*Pi^10*20^RootOf8+(-9231519020818020433920000000000*Pi^22+195541371952408496701440000000000*Pi^20+89300299589267320995840000000000*Pi^18-333503605675043554590720000000000*Pi^16-115500365322956203622400000000000*Pi^14+204706142659640339988480000000000*Pi^12+55783620627641021399040000000000*Pi^10-43454880575740151285760000000000*Pi^8-9286786763553830541120000000000*Pi^6-635208422610519981000000000000*Pi^4-16054449064166199375000000000*Pi^2-85686765999732421875000000)*_Z+(1683627180032000000000000000000*Pi^28+947040288768000000000000000000*Pi^26-243897798836910985052160000000000*Pi^24-105849518880314282213376000000000*Pi^22+543806205557386676011008000000000*Pi^20+206745517628405562998784000000000*Pi^18-493535946568048375234560000000000*Pi^16-161556685841710476165120000000000*Pi^14+209521703041307302907904000000000*Pi^12+57932333046211895115008000000000*Pi^10-32606166808014116503296000000000*Pi^8-7574931806403147431400000000000*Pi^6-916854325001083153125000000000*Pi^4-60848666758777034179687500000*Pi^2-1531121744500488281250000000)*_Z^2+(14538675656595603456000000000000*Pi^20+6360670599760576512000000000000*Pi^18-24363640065154351104000000000000*Pi^16-9459367828326973440000000000000*Pi^14+10040437028153917440000000000000*Pi^12+3693930616897744896000000000000*Pi^10+1609933205706216192000000000000*Pi^8+58674582771546096000000000000*Pi^6-1202653471578517170000000000000*Pi^4-149668239567146343750000000000*Pi^2-4663745768352832031250000000)*_Z^3+(-8723205391669003498291200000000*Pi^24-4361602695834501749145600000000*Pi^22+19490912047010429691494400000000*Pi^20+8825430454852624633036800000000*Pi^18-16301436833461042151424000000000*Pi^16-6564233354119088386867200000000*Pi^14+5977256592087501137510400000000*Pi^12+2106180608207148770918400000000*Pi^10-758124018049754123827200000000*Pi^8-240018107472837924480000000000*Pi^6-23564187036740637000000000000*Pi^4-997415989180706250000000000*Pi^2-15689219628471679687500000)*_Z^4-13647882752248245117187500000-261292721157421875*20^RootOf8) to be plotted but found name RootOf8

 

``


 

Download root_of.mw

 

hi

I want to mix two curve and have only one figure(I want to compare two curve in one plot domain )?

Thank you

plot.mw
 

h1 := solve(Vdc = 0.1500000000e-2*sqrt(2.53669508*10^8*u^3-6.06101011*10^8*u^2+3.46343435*10^8*u), u); plot([h1], Vdc = 0 .. 11.5, color = [magenta], thickness = 1); plot(Vector([0, 3.38, 5.21, 6.97, 8.4108, 10.099, 10.9232, 11.8091]), Vector([0, 0.760e-1, .1275, .1994, .2286, .3222, .3637, .999]), style = point, symbol = asterisk, color = "Blue")

 

 

``


 

Download plot.mw

 

 

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