Question

请问怎么用matlab的fsolve函数怎么求解这个方程呢？

方程如下：
(2*r - (8228485965250453*cos((pi*(a + 72))/180))/2251799813685248)/(4*(r^2 - (8228485965250453*cos((pi*(a + 72))/180)*r)/2251799813685248 + 7517095976830443/2251799813685248)^(1/2)) - (2*r - (8228485965250453*cos((pi*(a - 72))/180))/2251799813685248)/(4*(r^2 - (8228485965250453*cos((pi*(a - 72))/180)*r)/2251799813685248 + 7517095976830443/2251799813685248)^(1/2)) - (2*sin((pi*(a - 6))/180) - 2*r + (8228485965250453*sin((pi*(a + 6))/180))/2251799813685248)/(2*(r^2 - (8228485965250453*r*sin((pi*(a + 6))/180))/2251799813685248 - 2*r*sin((pi*(a - 6))/180) + 17817569595097215/2251799813685248)^(1/2)) - (2*r - (8228485965250453*cos((pi*(a - 144))/180))/2251799813685248)/(4*(r^2 - (8228485965250453*cos((pi*(a - 144))/180)*r)/2251799813685248 + 7517095976830443/2251799813685248)^(1/2)) - (2*r - (8228485965250453*cos((pi*(a + 144))/180))/2251799813685248)/(4*(r^2 - (8228485965250453*cos((pi*(a + 144))/180)*r)/2251799813685248 + 7517095976830443/2251799813685248)^(1/2)) - (2*r - (8228485965250453*cos((pi*a)/180))/2251799813685248)/(4*(r^2 - (8228485965250453*cos((pi*a)/180)*r)/2251799813685248 + 7517095976830443/2251799813685248)^(1/2))=0；
其中r是自变量，a是一个已知变量。我希望得到的结果里面r是由a和其他常数表示的。求大神解答。高分求解答。如果不用fsolve函数解决的也可以，求助

Answer 1

满满的字，看着就怕。。。
（1）先将你的算式中的r用x(1)代替，a用x(2)代替。然后在前面加上f=@(x)并去掉后面的=0
（2）根据你的几何意义，找出一个满足你要求的可能点，比如r=1,a=0（或你的初始条件）（在全域可能具有无穷多解。给出初始点后，fslove将在这个点附近找满足方程的最近的一个解）
（3）运行fsolve(f,[1,0])，其中[1,0]为我找的初始条件，要按照[r,a]格式的都可以
全部程序如下
f=@(x)(2.*x(1) - (8228485965250453.*cos((pi.*(x(2) + 72))./180))./2251799813685248)./(4.*(x(1).^2 - (8228485965250453.*cos((pi.*(x(2) + 72))./180).*x(1))./2251799813685248 + 7517095976830443./2251799813685248).^(1./2)) - (2.*x(1) - (8228485965250453.*cos((pi.*(x(2) - 72))./180))./2251799813685248)./(4.*(x(1).^2 - (8228485965250453.*cos((pi.*(x(2) - 72))./180).*x(1))./2251799813685248 + 7517095976830443./2251799813685248).^(1./2)) - (2.*sin((pi.*(x(2) - 6))./180) - 2.*x(1) + (8228485965250453.*sin((pi.*(x(2) + 6))./180))./2251799813685248)./(2.*(x(1).^2 - (8228485965250453.*x(1).*sin((pi.*(x(2) + 6))./180))./2251799813685248 - 2.*x(1).*sin((pi.*(x(2) - 6))./180) + 17817569595097215./2251799813685248).^(1./2)) - (2.*x(1) - (8228485965250453.*cos((pi.*(x(2) - 144))./180))./2251799813685248)./(4.*(x(1).^2 - (8228485965250453.*cos((pi.*(x(2) - 144))./180).*x(1))./2251799813685248 + 7517095976830443./2251799813685248).^(1./2)) - (2.*x(1) - (8228485965250453.*cos((pi.*(x(2) + 144))./180))./2251799813685248)./(4.*(x(1).^2 - (8228485965250453.*cos((pi.*(x(2) + 144))./180).*x(1))./2251799813685248 + 7517095976830443./2251799813685248).^(1./2)) - (2.*x(1) - (8228485965250453.*cos((pi.*x(2))./180))./2251799813685248)./(4.*(x(1).^2 - (8228485965250453.*cos((pi.*x(2))./180).*x(1))./2251799813685248 + 7517095976830443./2251799813685248).^(1./2));
x0=fsolve(f,[1,0]);x0为解