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thanks...

leosh 5
December 04 2015
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@tomleslie  thanks for your helping but what is z mean in solution,it isnt real number?

equ1 := -l*cos(xi)^2*(1-cos(beta__f))/(alpha^2*sin(sigma))-lambda__2*w*v^2*sin(sigma)/(g*l*cos(xi)^2) = 0;

-l*cos(xi)^2*(1-cos(beta__f))/(alpha^2*sin(sigma))-lambda__2*w*v^2*sin(sigma)/(g*l*cos(xi)^2) = 0

 (1)

equ2 := -l*cos(xi)^2*(1-cos(beta__f))/(alpha*sin(sigma)*tan(sigma))+l*cos(xi)^2*z__0*sin(beta__f)/(2*alpha*sin(sigma)*l*cos(sigma)^2)-lambda__1*L*sin(sigma)*cos(xi)+lambda__2*L*cos(sigma)*cos(xi)-lambda__2*w*alpha*v^2*sin(sigma)/(g*l*tan(sigma)*cos(xi)^2);

-l*cos(xi)^2*(1-cos(beta__f))/(alpha*sin(sigma)*tan(sigma))+(1/2)*cos(xi)^2*z__0*sin(beta__f)/(alpha*sin(sigma)*cos(sigma)^2)-lambda__1*L*sin(sigma)*cos(xi)+lambda__2*L*cos(sigma)*cos(xi)-lambda__2*w*alpha*v^2*sin(sigma)/(g*l*tan(sigma)*cos(xi)^2)

 (2)

equ3 := l*cos(xi)^2*sin(beta__f)*tan(sigma)/(2*alpha*sin(sigma)*l) = 0;

(1/2)*cos(xi)^2*sin(beta__f)*tan(sigma)/(alpha*sin(sigma)) = 0

 (3)

equ4 := -lambda__1*L*cos(sigma)*sin(xi)+lambda__2*L*sin(sigma)*sin(xi)-2*lambda__2*tan(xi)*w*alpha*v^2*sin(sigma)/(g*l*cos(xi)^2)-l*sin(2*xi)*(1-cos(beta__f))/(alpha*sin(sigma)) = 0;

-lambda__1*L*cos(sigma)*sin(xi)+lambda__2*L*sin(sigma)*sin(xi)-2*lambda__2*tan(xi)*w*alpha*v^2*sin(sigma)/(g*l*cos(xi)^2)-l*sin(2*xi)*(1-cos(beta__f))/(alpha*sin(sigma)) = 0

 (4)

equ5 := L*cos(sigma)*cos(xi)-w = 0;

L*cos(sigma)*cos(xi)-w = 0

 (5)

equ6 := L*sin(sigma)*cos(xi)-w*alpha*v^2*sin(sigma)/(g*l*cos(xi)^2);

L*sin(sigma)*cos(xi)-w*alpha*v^2*sin(sigma)/(g*l*cos(xi)^2)

 (6)

answer := solve({equ1, equ2, equ3, equ4, equ5, equ6}, {alpha, beta__f, sigma, xi, lambda__1, lambda__2})

{alpha = -L*g*l/(v^2*w), beta__f = 0, sigma = arctan(RootOf(-L^2+_Z^2+w^2)/L, -w/L), xi = Pi, lambda__1 = 0, lambda__2 = 0}, {alpha = L*g*l/(v^2*w), beta__f = Pi, sigma = arctan(RootOf(-L^2+_Z^2+w^2)/L, w/L), xi = 0, lambda__1 = -2*v^2*w^2/((L^2-w^2)*g*RootOf(-L^2+_Z^2+w^2)), lambda__2 = -2*v^2*w/((L^2-w^2)*g)}, {alpha = -L*g*l/(v^2*w), beta__f = Pi, sigma = arctan(RootOf(-L^2+_Z^2+w^2)/L, -w/L), xi = Pi, lambda__1 = 2*v^2*w^2/((L^2-w^2)*g*RootOf(-L^2+_Z^2+w^2)), lambda__2 = -2*v^2*w/((L^2-w^2)*g)}, {alpha = cos(xi)^3*L*g*l/(v^2*w), beta__f = 0, sigma = arctan(RootOf(-L^2*cos(xi)^2+_Z^2+w^2)/(L*cos(xi)), w/(L*cos(xi))), xi = xi, lambda__1 = 0, lambda__2 = 0}, {alpha = 2*RootOf(_Z^2-2)*w^2*g*l/(L^2*v^2), beta__f = Pi, sigma = arctan(RootOf(_Z^2-2), RootOf(_Z^2-2)), xi = arctan(RootOf(-L^2+_Z^2+2*w^2)/L, RootOf(_Z^2-2)*w/L), lambda__1 = -2*v^2/(w*g), lambda__2 = -2*v^2/(w*g)}, {alpha = 2*RootOf(_Z^2-2)*w^2*g*l/(L^2*v^2), beta__f = Pi, sigma = arctan(-(1/2)*RootOf(_Z^2-2), (1/2)*RootOf(_Z^2-2)), xi = arctan(RootOf(-L^2+_Z^2+2*w^2)/L, RootOf(_Z^2-2)*w/L), lambda__1 = 2*v^2/(w*g), lambda__2 = -2*v^2/(w*g)}

 (7)

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