如何用Matlab求参数方程的导数？

Question

已知参数方程x = a * cos(t) ^ 3，y = b * sin(t) ^ 3，用Matlab求dy / dx。如果直接使用：——————————————————————syms a b t;x = a * cos(t) ^ 3;y = b * sin(t) ^ 3;diff(y, 'x')——————————————————————进行计算的话，会得到：——————————————————————ans = 0——————————————————————

Answer 1

clear;clc;

syms a b t;

x = a * cos(t) ^ 3;

y = b * sin(t) ^ 3;

dydx=diff(y,t)/diff(x,t)

%%以下为图形验证

a=2;b=3;

x=str2func(['@(t)',vectorize(subs(x))]);

y=str2func(['@(t)',vectorize(subs(y))]);

k=str2func(['@(t)',vectorize(subs(dydx))]);

t=linspace(-pi,pi);

X=[-a,a];

n=0;

f=figure;

while isvalid(f)

n=mod(n,99)+1;

T=t(n);

hold off

plot(x(t),y(t));

hold on

Y=k(T)*(X-x(T))+y(T);

plot(X,Y);

plot(x(T),y(T),'ko','markerfacecolor','w');

xlim([-a,a])

ylim([-b,b])

pause(0.02)

end

Answer 2

syms a b t;
x = a * cos(t)^3;
y = b * sin(t)^3;

dx1dt = diff(x,t);

% 一阶导数
dy1dx = diff(y,t)/dx1dt

% 二阶导数
dy2d2x = diff(dy1dx,t)/dx1dt

% 3阶导数
dy3d3x = diff(dy2d2x,t)/dx1dt