Question

matlab多组非线性方程求多组解出错

[h,T1,T2,T3,T4,T5,T6,theta1,theta2,theta3,theta4,theta5,theta6,alpha1,alpha2,alpha3,alpha4,alpha5,b,a]=solve('T1*cos(theta1)==1025*9.8*pi*h','0.625*2*144*(2-h)==T1*sin(theta1)','1025*9.8*pi*0.025^2+T1*cos(theta1)==T2*cos(theta2)+98','T1*sin(theta1)==T2*sin(theta2)','T1*sin(pi/2-theta1-theta2)==1/2*(T1*cos(theta1)-T2*cos(theta2))*cos(alpha1)','T2*sin((alpha1+theta2-pi/2)/2)==1/2*(T1*cos(theta1)-T2*cos(theta2))*cos(alpha1)','1025*9.8*pi*0.025^2+T2*cos(theta2)==T3*cos(theta3)+98','T2*sin(theta2)==T3*sin(theta3)','T2*sin(pi/2-theta2-theta3)==1/2*(T2*cos(theta2)-T3*cos(theta3))*cos(alpha2)','T3*sin((alpha2+theta3-pi/2)/2)==1/2*(T2*cos(theta2)-T3*cos(theta3))*cos(alpha2)','1025*9.8*pi*0.025^2+T3*cos(theta3)==T4*cos(theta4)+98','T3*sin(theta3)==T4*sin(theta4)','T3*sin(pi/2-theta3-theta4)==1/2*(T3*cos(theta3)-T4*cos(theta4))*cos(alpha3)','T4*sin((alpha3+theta4-pi/2)/2)==1/2*(T3*cos(theta3)-T4*cos(theta4))*cos(alpha3)','1025*9.8*pi*0.025^2+T4*cos(theta4)==T5*cos(theta5)+98','T4*sin(theta4)==T5*sin(theta5)','T4*sin(pi/2-theta4-theta5)==1/2*(T4*cos(theta4)-T5*cos(theta5))*cos(alpha4)','T5*sin((alpha4+theta5-pi/2)/2)==1/2*(T4*cos(theta4)-T5*cos(theta5))*cos(alpha4)','1025*9.8*0.15^2+T5*cos(theta5)==12740-120540/78+T6*cos(theta6)','T5*sin(theta5)==T6*sin(theta6)','T5*sin(pi/2-alpha5-theta5)==1/2*(12740-120540/78-1025*9.8*0.15^2)*cos(alpha5)','T6*sin((alpha5+theta6-pi/2)/2)==1/2*(12740-120540/78-1025*9.8*0.15^2)*cos(alpha5)','18-h-(cos(alpha1)+cos(alpha2)+cos(alpha3)+cos(alpha4)+cos(alpha5))==T6*cos(theta6)/7*(exp(7*(b-a)/(T6*cos(theta6))-1)+exp(-7*(b-a)/(T6*cos(theta6))+1))/2','1/cos(theta6)==(exp(7*(b-a)/(T6*cos(theta6)))+exp(-7*(b-a)/(T6*cos(theta6))))/2','22.05=T6*cos(theta6)/7*(exp(7*(b-a)/(T6*cos(theta6)))- exp(-7*(b-a)/(T6*cos(theta6))))/2+a')
警告: Cannot find explicit solution.
> In solve at 319

h =

Empty sym: 0-by-1

T1 =

Empty sym: 0-by-1

T2 =

Empty sym: 0-by-1

T3 =

Empty sym: 0-by-1

T4 =

Empty sym: 0-by-1

T5 =

Empty sym: 0-by-1

T6 =

Empty sym: 0-by-1

theta1 =

Empty sym: 0-by-1

theta2 =

Empty sym: 0-by-1

theta3 =

Empty sym: 0-by-1

theta4 =

Empty sym: 0-by-1

theta5 =

Empty sym: 0-by-1

theta6 =

Empty sym: 0-by-1

alpha1 =

Empty sym: 0-by-1

alpha2 =

Empty sym: 0-by-1

alpha3 =

Empty sym: 0-by-1

alpha4 =

Empty sym: 0-by-1

alpha5 =

Empty sym: 0-by-1

b =

Empty sym: 0-by-1

a =

Empty sym: 0-by-1

Answer 1

运行你的代码后发现，因为方程数（25个）比变量数（20个）多，所以用solve()函数无法求解，只能给出空解（无解）。