写出xb, yb关于变量t的函数表达式

xe=31
ye=36
xc=19cos（2t）
yc=19sin（2t）
（xb-xc）^2+（yb-yc）^2=43^2
（xe-xf）^2+（ye-yf）^2=17^2
（yb-yc）（ye-yf）+（xb-xc）（xe-xf）=0
（yb-yc）（xf-xc）-（xb-xc）（yf-yc）=0

解题思路：

解题思路里基本上求解出来了，有四种解，用MATLAB仿真的结果如下：
xb对应的曲线

yb对应的曲线

b点的轨迹

代码：
clear;
close all;
clc;
xe=31;
ye= 36;
N=0.5;
t=-piN:0.01:piN;
xc=19cos(2t);
yc=19sin(2t);
R1=43;
R2=17;
% aa = (xb-xc)^2+(yb-yc)^2-43^2;
% bb = (xe-xf)^2+(ye-yf)^2-17^2;
% cc = (yb-yc)(ye-yf)+(xb-xc)(xe-xf);
% dd = (yb-yc)(xf-xc)-(xb-xc)(yf-yc);

a = R2;
b = xe-xc;
c = ye-yc;
delta = b.^2+c.^2-a^2;

%% alpha-90
x1 = (-2b-delta)./(2(a+c));
x2 = (-2b+delta)./(2(a+c));
x3 = (2b-delta)./(2(a-c));
x4 = (2b+delta)./(2(a-c));

alpha1 = 2atand(x1);
alpha2 = 2atand(x2);
alpha3 = 2atand(x3);
alpha4 = 2atand(x4);

xb1 = xc+R1cosd(alpha1);
yb1 = yc+R1sind(alpha1);
xb2 = xc+R1cosd(alpha2);
yb2 = yc+R1sind(alpha2);
xb3 = xc+R1cosd(alpha3);
yb3 = yc+R1sind(alpha3);
xb4 = xc+R1cosd(alpha4);
yb4 = yc+R1sind(alpha4);

figure;
plot(t,delta);

figure;
plot(xb1,yb1);
% figure;
% plot(t,alpha1);
% hold on;
% plot(t,alpha2);
% plot(t,alpha3);
% plot(t,alpha4);
% legend('1','2','3','4');
figure;
plot(t,xb1);
hold on;
plot(t,xb2);
plot(t,xb3);
plot(t,xb4);
legend('1','2','3','4');
title('t-xb')
hold off;

figure;
plot(t,yb1);
hold on;
plot(t,yb2);
plot(t,yb3);
plot(t,yb4);
legend('1','2','3','4');
title('t-yb')
hold off;

figure;
plot(xb1,yb1);
hold on;
plot(xb2,yb2);
plot(xb3,yb3);
plot(xb4,yb4);
title('轨迹')
legend('1','2','3','4');
hold off;

函数表达式，这个方便的话最好拍下图片，这个看着有点不太容易理解。

期待答案.,,,,

期待答案.,,,,

硬解的话真心。。。
这是个题目，还是个应用，能不能把题干给一下，看看有没有其他解法

看看这篇文档，是否能帮到你
https://ntrs.nasa.gov/api/citations/20040031532/downloads/20040031532.pdf