运用牛顿迭代法计算公式(exp(thetae-thetah)*tan(phi))/(sin(alpha-thetaa))=(tan(thetab)*cos(thetah))/(sin(alpha-thetae)*sin(thetaa));中的thetae,并使输出结果为角度值,编写为matlab代码
时间: 2024-02-17 19:02:22 浏览: 174
下面是使用matlab实现牛顿迭代法求解thetae的代码,其中假设给定的参数值为:
```matlab
thetah = 1.2;
phi = 0.3;
alpha = 0.8;
thetaa = 1.5;
thetab = 0.7;
```
代码如下:
```matlab
% 定义函数f(thetae)
function y = f(thetae)
global thetah phi alpha thetaa thetab
exp_part = exp(thetae - thetah) * tan(phi);
sin_part = sin(alpha - thetaa);
tan_part = tan(thetab) * cos(thetah);
sin2_part = sin(alpha - thetae) * sin(thetaa);
y = exp_part / sin_part - tan_part / sin2_part;
end
% 定义函数f'(thetae)
function y = fp(thetae)
global thetah phi alpha thetaa thetab
exp_part = exp(thetae - thetah) * tan(phi);
cos_part = cos(alpha - thetae);
sin_part = sin(thetaa);
tan_part = tan(thetab) * cos(thetah);
sin2_part = sin(alpha - thetae) * sin(thetaa);
cos2_part = cos(thetae) ^ 2;
y = -exp_part * cos_part * sin_part / sin_part ^ 2 - tan_part * cos_part / sin2_part ^ 2;
end
% 初始值和迭代精度
thetae_0 = 0.5;
eps = 1e-6;
% 迭代计算thetae
global thetah phi alpha thetaa thetab
thetae_n = thetae_0;
while true
thetae_np1 = thetae_n - f(thetae_n) / fp(thetae_n);
if abs(thetae_np1 - thetae_n) < eps
break;
end
thetae_n = thetae_np1;
end
% 输出结果
thetae_deg = thetae_np1 / pi * 180;
disp(thetae_deg);
```
其中,使用global关键字将参数thetah、phi、alpha、thetaa和thetab声明为全局变量,以便在函数中使用。
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