1、如下公式: 其中x、y、m、n为参数,a、b为未知数,利用MATLAB求解方程;
syms x y m n a b;
[a,b]=solve('x=m*cos(a)+n*cos(a+b)','y=m*sin(a)+n*sin(a+b)','a','b');
会得到四组解;对a(3)、b(3)、a(4)、b(4)进行化简,
simplify(a(3));
simplify(b(3));
simplify(a(4));
simplify(a(4));
得到:
a(3)= 2*atan((2*m*y - (- m^4 + 2*m^2*n^2 + 2*m^2*x^2 + 2*m^2*y^2 - n^4 + 2*n^2*x^2 + 2*n^2*y^2 - x^4 - 2*x^2*y^2 - y^4)^(1/2))/(m^2 + 2*m*x - n^2 + x^2 + y^2));
b(3)= 2*atan(((- m^2 + 2*m*n - n^2 + x^2 + y^2)*(m^2 + 2*m*n + n^2 - x^2 - y^2))^(1/2)/(- m^2 + 2*m*n - n^2 + x^2 + y^2));
a(4)= 2*atan((2*m*y + (- m^4 + 2*m^2*n^2 + 2*m^2*x^2 + 2*m^2*y^2 - n^4 + 2*n^