Question

用matlab解方程:n=a*cos(i)+b*cos(i+j);m=a*sin(i)+b*sin(i+j),解出i,j

Answer 1

用solve（）函数求解。
syms n m a b x y
s=solve(a*cos(x)+b*cos(x+y)-n,a*sin(x)+b*sin(x+y)-m,'x','y');
s.x % i 值
ans =
atan(-1/2*(n/(4*m^2+4*n^2)*(4*a^2*n+4*n^3+4*m^2*n-4*n*b^2+4*(-2*m^4*n^2-n^4*m^2-a^4*m^2-b^4*m^2-m^6+2*n^2*a^2*m^2+2*n^2*b^2*m^2+2*a^2*b^2*m^2+2*m^4*a^2+2*m^4*b^2)^(1/2))-m^2-n^2-a^2+b^2)/a/m,1/2/(4*m^2+4*n^2)*(4*a^2*n+4*n^3+4*m^2*n-4*n*b^2+4*(-2*m^4*n^2-n^4*m^2-a^4*m^2-b^4*m^2-m^6+2*n^2*a^2*m^2+2*n^2*b^2*m^2+2*a^2*b^2*m^2+2*m^4*a^2+2*m^4*b^2)^(1/2))/a)
atan(-1/2*(n/(4*m^2+4*n^2)*(4*a^2*n+4*n^3+4*m^2*n-4*n*b^2-4*(-2*m^4*n^2-n^4*m^2-a^4*m^2-b^4*m^2-m^6+2*n^2*a^2*m^2+2*n^2*b^2*m^2+2*a^2*b^2*m^2+2*m^4*a^2+2*m^4*b^2)^(1/2))-m^2-n^2-a^2+b^2)/a/m,1/2/(4*m^2+4*n^2)*(4*a^2*n+4*n^3+4*m^2*n-4*n*b^2-4*(-2*m^4*n^2-n^4*m^2-a^4*m^2-b^4*m^2-m^6+2*n^2*a^2*m^2+2*n^2*b^2*m^2+2*a^2*b^2*m^2+2*m^4*a^2+2*m^4*b^2)^(1/2))/a)
s.y % j 值
ans =
atan(-(1/2/(4*m^2+4*n^2)*(4*a^2*n+4*n^3+4*m^2*n-4*n*b^2+4*(-2*m^4*n^2-n^4*m^2-a^4*m^2-b^4*m^2-m^6+2*n^2*a^2*m^2+2*n^2*b^2*m^2+2*a^2*b^2*m^2+2*m^4*a^2+2*m^4*b^2)^(1/2))*a^2+1/2/(4*m^2+4*n^2)*(4*a^2*n+4*n^3+4*m^2*n-4*n*b^2+4*(-2*m^4*n^2-n^4*m^2-a^4*m^2-b^4*m^2-m^6+2*n^2*a^2*m^2+2*n^2*b^2*m^2+2*a^2*b^2*m^2+2*m^4*a^2+2*m^4*b^2)^(1/2))*n^2+1/2/(4*m^2+4*n^2)*(4*a^2*n+4*n^3+4*m^2*n-4*n*b^2+4*(-2*m^4*n^2-n^4*m^2-a^4*m^2-b^4*m^2-m^6+2*n^2*a^2*m^2+2*n^2*b^2*m^2+2*a^2*b^2*m^2+2*m^4*a^2+2*m^4*b^2)^(1/2))*m^2-1/2/(4*m^2+4*n^2)*(4*a^2*n+4*n^3+4*m^2*n-4*n*b^2+4*(-2*m^4*n^2-n^4*m^2-a^4*m^2-b^4*m^2-m^6+2*n^2*a^2*m^2+2*n^2*b^2*m^2+2*a^2*b^2*m^2+2*m^4*a^2+2*m^4*b^2)^(1/2))*b^2-2*a^2*n)*m/a/b/(n/(4*m^2+4*n^2)*(4*a^2*n+4*n^3+4*m^2*n-4*n*b^2+4*(-2*m^4*n^2-n^4*m^2-a^4*m^2-b^4*m^2-m^6+2*n^2*a^2*m^2+2*n^2*b^2*m^2+2*a^2*b^2*m^2+2*m^4*a^2+2*m^4*b^2)^(1/2))-m^2-n^2-a^2+b^2),-1/2/a*(-n^2-m^2+a^2+b^2)/b)
atan(-(1/2/(4*m^2+4*n^2)*(4*a^2*n+4*n^3+4*m^2*n-4*n*b^2-4*(-2*m^4*n^2-n^4*m^2-a^4*m^2-b^4*m^2-m^6+2*n^2*a^2*m^2+2*n^2*b^2*m^2+2*a^2*b^2*m^2+2*m^4*a^2+2*m^4*b^2)^(1/2))*a^2+1/2/(4*m^2+4*n^2)*(4*a^2*n+4*n^3+4*m^2*n-4*n*b^2-4*(-2*m^4*n^2-n^4*m^2-a^4*m^2-b^4*m^2-m^6+2*n^2*a^2*m^2+2*n^2*b^2*m^2+2*a^2*b^2*m^2+2*m^4*a^2+2*m^4*b^2)^(1/2))*n^2+1/2/(4*m^2+4*n^2)*(4*a^2*n+4*n^3+4*m^2*n-4*n*b^2-4*(-2*m^4*n^2-n^4*m^2-a^4*m^2-b^4*m^2-m^6+2*n^2*a^2*m^2+2*n^2*b^2*m^2+2*a^2*b^2*m^2+2*m^4*a^2+2*m^4*b^2)^(1/2))*m^2-1/2/(4*m^2+4*n^2)*(4*a^2*n+4*n^3+4*m^2*n-4*n*b^2-4*(-2*m^4*n^2-n^4*m^2-a^4*m^2-b^4*m^2-m^6+2*n^2*a^2*m^2+2*n^2*b^2*m^2+2*a^2*b^2*m^2+2*m^4*a^2+2*m^4*b^2)^(1/2))*b^2-2*a^2*n)*m/a/b/(n/(4*m^2+4*n^2)*(4*a^2*n+4*n^3+4*m^2*n-4*n*b^2-4*(-2*m^4*n^2-n^4*m^2-a^4*m^2-b^4*m^2-m^6+2*n^2*a^2*m^2+2*n^2*b^2*m^2+2*a^2*b^2*m^2+2*m^4*a^2+2*m^4*b^2)^(1/2))-m^2-n^2-a^2+b^2),-1/2/a*(-n^2-m^2+a^2+b^2)/b)

追问

你好，是这样的吗，

为什么我解不了？

追答

版本问题，我用的是Matlab 7.0