Question

MATLAB 求解含多个解的方程组

syms x y theta
eq1=(10-x-3*cos(theta))^2+(3-y-3*sin(theta))^2-5^2==0;
eq2=(1-x+3*cos(theta))^2+(2-y+3*cos(theta))^2-6^2==0;
eq3=((3-y-3*sin(theta))/(10-x-3*cos(theta)))+(2-y+3*cos(theta))/(1-x+3*cos(theta))-2*tan(theta)==0;
[x y theta]=solve(eq1,eq2,eq3,x,y,theta)

请问怎么显示多个解的近似值

Answer 1

(10-x-3*cosθ)^2+(3-y-3*sinθ)^2-5^2=0;①
(1-x+3*cosθ)^2+(2-y+3*cosθ)^2-6^2=0;②
((3-y-3*sinθ)/(10-x-3*cosθ))+(2-y+3*cosθ))/(1-x+3*cosθ))-2*tanθ=0;③
由②，(1-x)^2+6(1-x)cosθ+9cos^θ+(2-y)^2+6(2-y)cosθ+9cos^θ-36=0,
整理得18cos^θ+6(3-x-y)cosθ+x^2+y^2-2x-4y-31=0,
△/36=(3-x-y)^2-2(x^2+y^2-2x-4y-31)
=9-6(x+y)+(x+y)^2-2x^2-2y^2+4x+8y+62
=71-2x+2y-x^2+2xy-y^2
=-（x-y+1）^2+72,
所以cosθ=[x+y_3土√(71-2x+2y-x^2+2xy-y^2)]/6,④
由①，(10-x)^2-6(10-x)cosθ+(3-y)^2-6(3-y)sinθ-16=0,
整理得93-20x-6y+x^2+y^2-6(10-x)cosθ-6(3-y)sinθ=0,
把④代入上式得93-20x-6y+x^2+y^2-(10-x)[x+y-3土√(71-2x+2y-x^2+2xy-y^2)]-6(3-y)sinθ=0,
解得sinθ=……,⑤
④^2+⑤^2,消去θ，得⑥
把④⑤代入③，消去θ，得⑦。
由⑥⑦解得x,y.
代入④⑤，求θ。
仅供参考。