lab9

%syms t;
%
%x = @(t) 4 + 4*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 = input("Introduceti valoarea pentru t0");
%disp("Curbura este");
%disp(diff(k(t0)));
%x= diff(k(t0));
%
%if (x != 0)
%  disp("Nu este varf");
%else
%  disp("Este varf");
%endif

syms t;
x = @(t) 2+t+t^3;
y = @(t) -t-t^3;
z = @(t) 5+t^3;
ezplot3(x(t),y(t),z(t));

d1 = [diff(x(t)),diff(y(t)),diff(z(t))];
d2 = [diff(x(t),2),diff(y(t),2),diff(z(t),2)];
d3 = [diff(x(t),3),diff(y(t),3),diff(z(t),3)];
disp(d1);
disp(d2);
disp(d3);

k = simplify(norm(cross(d1,d2))/(norm(d1)^3));
disp(k);
tau = simplify((dot(cross(d1,d2),d3))/norm(cross(d1,d2))^2);
disp(tau);
disp("Verificare elice");
disp(tau/k);