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How do I solve a complex equation in fun...

noob 10 Maple
solve
January 14 2017
1 0

Guys,

I am not very familiar with Maple and have to solve quite a complex equation.

I have an equation which is complex ,containing I . I split this equation up in Re=0 an Im=0 . I have to get an answer in function of other parameters, in order to plot these... Maybe it s easier if you look at the work sheet


 

> 

restart
> 

with(LinearAlgebra):
> 

Student(NumericalAnalysis)

(module Student () description "a package to assist with the teaching and learning of standard undergraduate mathematics"; local ModuleLoad, localColors, GetColor, SelectColor, UpdateColor, GetCaption, colorNum, colorDefaults, Defaults, PlotOptionsWindow, InitAnimation, EndAnimation, DoPlayPause, IncrSpd, DecrSpd, Colours, CheckPoint, CheckRange, CheckTextField, CleanFloat, CombineRanges, EvaluateFunction, FindHRange, FindHRange3d, FindVRange, FindVRange3d, GetSpecPoints, EvaluateFunctionNumeric, EvaluateFunctionNumeric3d, VRangeCmp, MaximizePointList, MinimizePointList, FindHRange3dCrossSections, FindVRangeSymbolic, SymEvalFunc, SymLimits, FindAllSpecialPoints, FindHRangeRatPoly, GetRealDomain, GetTextField, GetVariable, IsColour, MapletGenericError, MapletNoInputError, MapletTypeError, ProcessCharacter, ProcessVisual, RequiredError, RemovePlotOptions, mapletColor, mapletDarkColor, mapletLightColor, mapletHelpColor, IsMac, ProcessColorNames; export _pexports, SetColors, SetDefault, SetDefaults, Precalculus, MultivariateCalculus, VectorCalculus, LinearAlgebra, Statistics, Calculus1, NumericalAnalysis, Basics; global x, y, z, r, t, p; option package, `Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2005`; end module)(NumericalAnalysis)

 (1)
> 

wn := 50

50

 (2)
> 

Np := 2

2

 (3)
> 

``
> 

``
> 

w0 := v0*wn

50*v0

 (4)
> 

V0 := 230*sqrt(2)

230*2^(1/2)

 (5)
> 

Ep0 := 1.5*V0

345.0*2^(1/2)

 (6)
> 

NULL
> 

delta := 0

0

 (7)
> 

phi[q0] := 0

0

 (8)
> 

Iq0 := 0

0

 (9)
> 

L := proc (p) options operator, arrow; Ls*(p*tau[r]+1)/(p*tau[r]/sigma+1) end proc

proc (p) options operator, arrow; Ls*(p*tau[r]+1)/(p*tau[r]/sigma+1) end proc

 (10)
> 

Rs := 2.43

2.43

 (11)
> 

Rr := 2.43

2.43

 (12)
> 

Lr := 0.12e-1+.237

.249

 (13)
> 

Ls := Lr

.249

 (14)
> 

M := sqrt(.92*Ls^2)

.2388324099

 (15)
> 

sigma := 1-M^2/(Ls*Lr)

0.799999996e-1

 (16)
> 

``
> 

tau[r] := sigma*Lr*wn/Rr

.4098765412

 (17)
> 

tau[s] := sigma*Ls*wn/Rs

.4098765412

 (18)
> 

alpha := tau[r]/tau[s]

1.000000000

 (19)
> 

``
> 

``
> 

``
> 

``
> 

assume(v0, 'real', nu, 'real')
> 

``

345.0*2^(1/2)

 (20)
> 

phi[d0] := Ls*Id0-Ep0/w0

.249*Id0-6.900000000*2^(1/2)/v0

 (21)
> 

Vd0 := V0*sin(delta)

0

 (22)
> 

Vq0 := V0*cos(delta)

230*2^(1/2)

 (23)
> 

Id0 := (Rs*Vd0-wn*v0*Ls*(Vq0-Ep0))/(Ls^2*w0^2+Rs^2)

1431.7500*v0*2^(1/2)/(155.002500*v0^2+5.9049)

 (24)
> 

Dp := (Rs+p*wn*L(p))^2+v0*wn^2*L(p)^2

(2.43+12.450*p*(.4098765412*p+1)/(5.123456791*p+1))^2+155.002500*v0*(.4098765412*p+1)^2/(5.123456791*p+1)^2

 (25)
> 

simplify(Dp)

(26.04023075*p^4+254.1275544*p^3+(644.8103998+26.04023074*v0)*p^2+(121.014+127.0637772*v0)*p+5.9049+155.0025*v0)/(5.123456791*p+1.)^2

 (26)
> 

N := -(3/2)*Np*[[L(p)^2*(Id0*phi[d0]+Iq0*phi[q0])-L(p)*(phi[d0]^2-phi[q0]^2)]*(p^2+v0^2)*wn^2+Rs*[p*L(p)^2*(Id0^2+Iq0^2)-p*(phi[d0]^2+phi[q0]^2)]*wn+Rs^2*[L(p)*Iq0^2+L(p)*Id0^2-Id0*phi[d0]-Iq0*phi[q0]]]

[-7500*[88.76993175*(.4098765412*p+1)^2*v0*2^(1/2)*(356.5057500*v0*2^(1/2)/(155.002500*v0^2+5.9049)-6.900000000*2^(1/2)/v0)/((5.123456791*p+1)^2*(155.002500*v0^2+5.9049))-.249*(.4098765412*p+1)*(356.5057500*v0*2^(1/2)/(155.002500*v0^2+5.9049)-6.900000000*2^(1/2)/v0)^2/(5.123456791*p+1)]*(p^2+v0^2)+[-18084126.16*(.4098765412*p+1)*v0^2/((5.123456791*p+1)*(155.002500*v0^2+5.9049)^2)+25363.02172*v0*2^(1/2)*(356.5057500*v0*2^(1/2)/(155.002500*v0^2+5.9049)-6.900000000*2^(1/2)/v0)/(155.002500*v0^2+5.9049)-92653238.97*p*(.4098765412*p+1)^2*v0^2/((5.123456791*p+1)^2*(155.002500*v0^2+5.9049)^2)+364.5000000*p*(356.5057500*v0*2^(1/2)/(155.002500*v0^2+5.9049)-6.900000000*2^(1/2)/v0)^2]]

 (27)
> 

char := (p*J*wn^2/Np*p)*Dp+N

1250*p^2*J*((2.43+12.450*p*(.4098765412*p+1)/(5.123456791*p+1))^2+155.002500*v0*(.4098765412*p+1)^2/(5.123456791*p+1)^2)+[-7500*[88.76993175*(.4098765412*p+1)^2*v0*2^(1/2)*(356.5057500*v0*2^(1/2)/(155.002500*v0^2+5.9049)-6.900000000*2^(1/2)/v0)/((5.123456791*p+1)^2*(155.002500*v0^2+5.9049))-.249*(.4098765412*p+1)*(356.5057500*v0*2^(1/2)/(155.002500*v0^2+5.9049)-6.900000000*2^(1/2)/v0)^2/(5.123456791*p+1)]*(p^2+v0^2)+[-18084126.16*(.4098765412*p+1)*v0^2/((5.123456791*p+1)*(155.002500*v0^2+5.9049)^2)+25363.02172*v0*2^(1/2)*(356.5057500*v0*2^(1/2)/(155.002500*v0^2+5.9049)-6.900000000*2^(1/2)/v0)/(155.002500*v0^2+5.9049)-92653238.97*p*(.4098765412*p+1)^2*v0^2/((5.123456791*p+1)^2*(155.002500*v0^2+5.9049)^2)+364.5000000*p*(356.5057500*v0*2^(1/2)/(155.002500*v0^2+5.9049)-6.900000000*2^(1/2)/v0)^2]]

 (28)
> 

eval(char)

1250*p^2*J*((2.43+12.450*p*(.4098765412*p+1)/(5.123456791*p+1))^2+155.002500*v0*(.4098765412*p+1)^2/(5.123456791*p+1)^2)+[-7500*[88.76993175*(.4098765412*p+1)^2*v0*2^(1/2)*(356.5057500*v0*2^(1/2)/(155.002500*v0^2+5.9049)-6.900000000*2^(1/2)/v0)/((5.123456791*p+1)^2*(155.002500*v0^2+5.9049))-.249*(.4098765412*p+1)*(356.5057500*v0*2^(1/2)/(155.002500*v0^2+5.9049)-6.900000000*2^(1/2)/v0)^2/(5.123456791*p+1)]*(p^2+v0^2)+[-18084126.16*(.4098765412*p+1)*v0^2/((5.123456791*p+1)*(155.002500*v0^2+5.9049)^2)+25363.02172*v0*2^(1/2)*(356.5057500*v0*2^(1/2)/(155.002500*v0^2+5.9049)-6.900000000*2^(1/2)/v0)/(155.002500*v0^2+5.9049)-92653238.97*p*(.4098765412*p+1)^2*v0^2/((5.123456791*p+1)^2*(155.002500*v0^2+5.9049)^2)+364.5000000*p*(356.5057500*v0*2^(1/2)/(155.002500*v0^2+5.9049)-6.900000000*2^(1/2)/v0)^2]]

 (29)
> 

p := I*nu

I*nu

 (30)
> 

R := Re(char)

Re(-1250*nu^2*J*((2.43+(12.450*I)*nu*((.4098765412*I)*nu+1)/((5.123456791*I)*nu+1))^2+155.002500*v0*((.4098765412*I)*nu+1)^2/((5.123456791*I)*nu+1)^2)+[-7500*[88.76993175*((.4098765412*I)*nu+1)^2*v0*2^(1/2)*(356.5057500*v0*2^(1/2)/(155.002500*v0^2+5.9049)-6.900000000*2^(1/2)/v0)/(((5.123456791*I)*nu+1)^2*(155.002500*v0^2+5.9049))-.249*((.4098765412*I)*nu+1)*(356.5057500*v0*2^(1/2)/(155.002500*v0^2+5.9049)-6.900000000*2^(1/2)/v0)^2/((5.123456791*I)*nu+1)]*(-nu^2+v0^2)+[-18084126.16*((.4098765412*I)*nu+1)*v0^2/(((5.123456791*I)*nu+1)*(155.002500*v0^2+5.9049)^2)+25363.02172*v0*2^(1/2)*(356.5057500*v0*2^(1/2)/(155.002500*v0^2+5.9049)-6.900000000*2^(1/2)/v0)/(155.002500*v0^2+5.9049)-(92653238.97*I)*nu*((.4098765412*I)*nu+1)^2*v0^2/(((5.123456791*I)*nu+1)^2*(155.002500*v0^2+5.9049)^2)+(364.5000000*I)*nu*(356.5057500*v0*2^(1/2)/(155.002500*v0^2+5.9049)-6.900000000*2^(1/2)/v0)^2]])

 (31)
> 

im := Im(char)

Im(-1250*nu^2*J*((2.43+(12.450*I)*nu*((.4098765412*I)*nu+1)/((5.123456791*I)*nu+1))^2+155.002500*v0*((.4098765412*I)*nu+1)^2/((5.123456791*I)*nu+1)^2)+[-7500*[88.76993175*((.4098765412*I)*nu+1)^2*v0*2^(1/2)*(356.5057500*v0*2^(1/2)/(155.002500*v0^2+5.9049)-6.900000000*2^(1/2)/v0)/(((5.123456791*I)*nu+1)^2*(155.002500*v0^2+5.9049))-.249*((.4098765412*I)*nu+1)*(356.5057500*v0*2^(1/2)/(155.002500*v0^2+5.9049)-6.900000000*2^(1/2)/v0)^2/((5.123456791*I)*nu+1)]*(-nu^2+v0^2)+[-18084126.16*((.4098765412*I)*nu+1)*v0^2/(((5.123456791*I)*nu+1)*(155.002500*v0^2+5.9049)^2)+25363.02172*v0*2^(1/2)*(356.5057500*v0*2^(1/2)/(155.002500*v0^2+5.9049)-6.900000000*2^(1/2)/v0)/(155.002500*v0^2+5.9049)-(92653238.97*I)*nu*((.4098765412*I)*nu+1)^2*v0^2/(((5.123456791*I)*nu+1)^2*(155.002500*v0^2+5.9049)^2)+(364.5000000*I)*nu*(356.5057500*v0*2^(1/2)/(155.002500*v0^2+5.9049)-6.900000000*2^(1/2)/v0)^2]])

 (32)
> 

``
> 

simplify(im)

Im(((32550.28842*nu^4*J-(158829.7215*I)*nu^3*J-193753.125*nu^2*J)*v0-32550.28844*nu^6*J+(317659.4430*I)*nu^5*J+806012.9998*nu^4*J-(151267.5000*I)*nu^3*J+(-7381.125*J+[196873.5712*[-177.5398635*((.4098765412*I)*nu+1.)^2*(713.0115000*v0^2+40.74381000)/(((5.123456791*I)*nu+1.)^2*(155.002500*v0^2+5.9049)*(155.0025000*v0^2+5.904900000))-.4979999998*((.4098765412*I)*nu+1)*(713.0115*v0^2+40.74381)^2/(((5.123456791*I)*nu+1.)*v0^2*(155.0025*v0^2+5.9049)^2)]*(-nu^2+v0^2)+[474704866.5*((.4098765412*I)*nu+1)*v0^2/(((5.123456791*I)*nu+1.)*(155.002500*v0^2+5.9049)^2)-26.24980949*(-36168252.32*v0^2-2066772.276)/(155.0025*v0^2+5.9049)^2+(2432129872.*I)*nu*((.4098765412*I)*nu+1.)^2*v0^2/(((5.123456791*I)*nu+1.)^2*(155.002500*v0^2+5.9049)^2)-(19136.11111*I)*nu*(713.0115*v0^2+40.74381)^2/(v0^2*(155.0025*v0^2+5.9049)^2)]])*nu^2+(10.24691358*I)*[-7500*[-177.5398635*((.4098765412*I)*nu+1.)^2*(713.0115000*v0^2+40.74381000)/(((5.123456791*I)*nu+1.)^2*(155.002500*v0^2+5.9049)*(155.0025000*v0^2+5.904900000))-.4979999998*((.4098765412*I)*nu+1)*(713.0115*v0^2+40.74381)^2/(((5.123456791*I)*nu+1.)*v0^2*(155.0025*v0^2+5.9049)^2)]*(-nu^2+v0^2)+[-18084126.16*((.4098765412*I)*nu+1)*v0^2/(((5.123456791*I)*nu+1.)*(155.002500*v0^2+5.9049)^2)+(-36168252.32*v0^2-2066772.276)/(155.0025*v0^2+5.9049)^2-(92653238.97*I)*nu*((.4098765412*I)*nu+1.)^2*v0^2/(((5.123456791*I)*nu+1.)^2*(155.002500*v0^2+5.9049)^2)+(728.9999996*I)*nu*(713.0115*v0^2+40.74381)^2/(v0^2*(155.0025*v0^2+5.9049)^2)]]*nu+[-7500*[-177.5398635*((.4098765412*I)*nu+1.)^2*(713.0115000*v0^2+40.74381000)/(((5.123456791*I)*nu+1.)^2*(155.002500*v0^2+5.9049)*(155.0025000*v0^2+5.904900000))-.4979999998*((.4098765412*I)*nu+1)*(713.0115*v0^2+40.74381)^2/(((5.123456791*I)*nu+1.)*v0^2*(155.0025*v0^2+5.9049)^2)]*(-nu^2+v0^2)+[-18084126.16*((.4098765412*I)*nu+1)*v0^2/(((5.123456791*I)*nu+1.)*(155.002500*v0^2+5.9049)^2)+(-36168252.32*v0^2-2066772.276)/(155.0025*v0^2+5.9049)^2-(92653238.97*I)*nu*((.4098765412*I)*nu+1.)^2*v0^2/(((5.123456791*I)*nu+1.)^2*(155.002500*v0^2+5.9049)^2)+(728.9999996*I)*nu*(713.0115*v0^2+40.74381)^2/(v0^2*(155.0025*v0^2+5.9049)^2)]])/((5.123456791*I)*nu+1.)^2)

 (33)
> 

solve(im = 0)

Warning, solve may be ignoring assumptions on the input variables.

  

Error, (in Engine:-Dispatch) badly formed input to solve: not fully algebraic

  
> 

``
> 

``

Error, (in fsolve) b is in the equation, and is not solved for

  

-I*b/l

 (34)
> 

``


 

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