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文章目录
- 问题背景
- 代码
- my_fun.m
- main.m
- 结果展示:
- 不加入F(4)
- 加入F(4)
问题背景
求解方程组的时候，对某些未知数的求解结果的取值范围有要求。例如在某些物理问题求解中，要求待求解量大于0。
代码
一共两个文件:
my_fun.m
main.m
my_fun.m
function F=my_fun(x)
R = 10;
yinzi = pi/180;
alpha_ON = 50*yinzi;
alpha_OM = 10*yinzi;
alpha_MN = 40*yinzi;
F(1)=sin(alpha_ON)*sin(x(2))-sin(alpha_OM)*sin(x(3));
F(2)=2*sin((x(1)-1)*pi/9)*sin(alpha_ON)*cos((x(1)-1)*pi/9+x(2)) - sin(alpha_MN)*sin(x(3)+alpha_ON);
F(3)=x(2)+ 2*(x(1)-1)*pi/9- x(3) - alpha_MN;
difference = R/sin(alpha_OM)*sin(x(2)) - R;
tolerance = 1e-5;
if abs(difference) < toleranceF(4) = 0;
elseF(4) = difference;
end
end
核心是这里:
difference = R/sin(alpha_OM)*sin(x(2)) - R;
tolerance = 1e-5;
if abs(difference) < toleranceF(4) = 0;
elseF(4) = difference;
设置difference和tolerance，定义F(4),在求解过程中，会让F(4)等于0，也就是令
R s i n ( a l p h a O M ) × s i n ( x ( 2 ) ) = R \frac{R}{sin(alpha_{OM})} \times sin(x(2)) = R sin(alphaOM)R×sin(x(2))=R
这个条件逐渐满足。
main.m
%x0=[0,pi/18,5*pi/18];
x0 = zeros(1,3)
options.Display = 'iter';
R = 10;
result_x=fsolve(@my_fun,x0,options)
yinzi = pi/180;
alpha_ON = 50*yinzi;
alpha_OM = 10*yinzi;
alpha_MN = 40*yinzi;
pho_x = R/sin(alpha_OM)*sin(result_x(2))
结果展示:
不加入F(4)
result_x =1.6379 -0.0725 -0.3253pho_x =-4.1722
加入F(4)
result_x =2.9988 0.1745 0.8718pho_x =10.0000
这个解正确。