Question: Solving equation system

September 26 2012 EduardFerrer 0
Maple 16
0

Hello,

I'm really new in Maple so the problem I have may look somewhat trivial. I have to solve a system of equations for two variables (V and alpha). All the expressions shall be reduced at the end in three (Assuming that 2 of them will be dependent). The code I've written is:

> Vax := proc (V, alpha) options operator, arrow; V*cos*alpha-w*cos*(phiW-phi) end proc;
> Vay := proc (V, alpha) options operator, arrow; V*sin*alpha-w*sin*(phiW-phi) end proc;
> alphaA := proc (V, alpha) options operator, arrow; arctan(Vax(V, alpha)/Vay(V, alpha)) end proc;

> Vhx := proc (V, alpha) options operator, arrow; V*cos*alpha-c*cos*(phiC-phi) end proc;
> Vhy := proc (V, alpha) options operator, arrow; V*sin*alpha-c*sin*(phiC-phi) end proc;
> alphaH := proc (V, alpha) options operator, arrow; arctan(Vhy(V, alpha)/Vhx(V, alpha)) end proc;
> alphaS := proc (V, alpha) options operator, arrow; alphaA(V, alpha)-theta end proc;

> Cla := proc (V, alpha) options operator, arrow; .479425562873746+.149822152597990*alphaS(V, alpha)+(-1)*0.6088517201146e-2*alphaS(V, alpha)^2+0.66353328784e-4*alphaS(V, alpha)^3+0.411529411e-6*alphaS(V, alpha)^4+(-1)*0.11748785e-7*alphaS(V, alpha)^5+0.55243e-10*alphaS(V, alpha)^6 end proc;

> Cda := proc (V, alpha) options operator, arrow; .103443926664331+0.5088988381576e-2*alphaS*(V, alpha)+0.242254089150e-3*alphaS(V, alpha)^2+0.8260927215e-5*alphaS(V, alpha)^3+(-1)*0.353184433e-6*alphaS(V, alpha)^4+0.4053756e-8*alphaS(V, alpha)^5+(-1)*0.15453e-10*alphaS(V, alpha)^6 end proc;

> Clh := proc (V, alpha) options operator, arrow; -0.7884106963191e-2+.138129770559695*alphaH(V, alpha)+(-1)*0.4532146281278e-2*alphaH(V, alpha)^2+0.57751614720e-4*alphaH(V, alpha)^3+(-1)*0.290554655e-6*alphaH(V, alpha)^4+(-1)*0.265676e-9*alphaH(V, alpha)^5+0.5292e-11*alphaH(V, alpha)^6 end proc;

> Cdh := proc (V, alpha) options operator, arrow; .103443926664331+0.5088988381576e-2*alphaH(V, alpha)+0.242254089150e-3*alphaH(V, alpha)^2+0.8260927215e-5*alphaH(V, alpha)^3+(-1)*0.353184433e-6*alphaH(V, alpha)^4+0.4053756e-8*alphaH(V, alpha)^5+(-1)*0.15453e-10*alphaH(V, alpha)^6 end proc;
> Cma := proc (V, alpha) options operator, arrow; Xa*Cla(V, alpha)/la end proc;

> Cmh := proc (V, alpha) options operator, arrow; Xh*Clh(V, alpha)/lh+Cmb*beta end proc;

> La := proc (V, alpha) options operator, arrow; .5*roA*(Vax*(V, alpha)^2+Vay*(V, alpha)^2)*supA*Cla*(V, alpha) end proc;
> Da := proc (V, alpha) options operator, arrow; .5*roA*(Vax*(V, alpha)^2+Vay*(V, alpha)^2)*supA*Cda*(V, alpha) end proc;
> Lh := proc (V, alpha) options operator, arrow; .5*roH*(Vhx*(V, alpha)^2+Vhy*(V, alpha)^2)*supH*Clh*(V, alpha) end proc;
> Dh := proc (V, alpha) options operator, arrow; .5*roH*(Vhx*(V, alpha)^2+Vhy*(V, alpha)^2)*supH*Cdh*(V, alpha) end proc;
> Ma := proc (V, alpha) options operator, arrow; .5*roA*(Vax*(V, alpha)^2+Vay*(V, alpha)^2)*supA*la*Cma*(V, alpha) end proc;

> Mh := proc (V, alpha) options operator, arrow; .5*roH*(Vhx*(V, alpha)^2+Vhy*(V, alpha)^2)*supH*lh*Cmh*(V, alpha) end proc;

> X := proc (V, alpha) options operator, arrow; La*(V, alpha)*sin(alphaA*(V, alpha))-Da*(V, alpha)*cos(alphaA*(V, alpha))+Lh*(V, alpha)*sin(alphaH*(V, alpha))-Dh*(V, alpha)*cos(alphaH*(V, alpha)) end proc;

> Y := proc (V, alpha) options operator, arrow; -La*(V, alpha)*cos(alphaA*(V, alpha))-Da*(V, alpha)*sin(alphaA*(V, alpha))-Lh*(V, alpha)*cos(alphaH*(V, alpha))-Dh*(V, alpha)*sin(alphaH*(V, alpha)) end proc;

> M := proc (V, alpha) options operator, arrow; Ma*(V, alpha)+Mh*(V, alpha) end proc;

> solve*({X(V, alpha) = 0, Y(V, alpha) = 0}, {V, alpha});

Can you see where it fails? Is there any easier and more compact option?

Thanks,

 

Edu Ferrer, Sant Cugat del Vallès (Barcelona)

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