lab7

syms t;
#x = @(t) t*cos(t);
#y = @(t) t*sin(t);

#xd =@(t) diff(x(t));
#yd =@(t) diff(y(t));
#g = ezplot(xd(t),yd(t));
#set(g,'Color','r');

#xdd = @(t) diff(xd(t));
#ydd = @(t) diff(yd(t));
#g = ezplot(xdd(t),ydd(t));
#set(g,'Color','r');
#x = @(t) 3*cos(t)^3;
#y = @(t) 2*sin(t)^3;
#g = ezplot(x(t),y(t));
#set(g,'Color','b');
#x = @(t) (sin(t)*(e^cos(t)-2*cos(4*t)+sin(t/12)^5));
#y = @(t) (cos(t)*(e^cos(t)-2*cos(4*t)+sin(t/12)^5));
#g = ezplot(x(t),y(t));
#set(g,'Color','b');

x = @(t) 4+2*cos(t);
y = @(t) 1+4*sin(t);
c = @(t) [x(t),y(t)];
v = [diff(x(t)),diff(y(t))];
a = [diff(x(t),2),diff(y(t),2)];
ezplot(x(t),y(t));
k = @(t) det([v;a])/sqrt(sum(v.^2))^3;
disp("Curbura lui e in c(t)");
disp(k(t));
R= @(t) 1/abs(k(t));
disp("raza de curbura in c(t)");
disp(R(t));
t0=pi/3;
disp("Curbura in c(pi/3)");
disp(subs(k,t,t0));
disp("raza de curbura in c(pi/3)");
disp(subs(R,t,t0));