% ECE 463 Lecture #6
% calling routine for ball rolling in a bowl

x = 1.5;
dx = 0;
g = 9.8;

dt = 0.01;
t = 0;
L = 0;
while(t < 100)

% Compute the dynamics
 ddx = - (1.4*dx*dx + g)*x / ( 1.4*(1 + x*x));
 
% Integrate
 x  = x  + dx  * dt;
 dx = dx + ddx * dt;
 dy = x*dx;
 dL = sqrt(1 + (dy/dx)^2) * dx;
 L = L + dL * dt;
 t  = t  + dt;
 
% Display the ball
 y = 0.5 * x^2;

 x1 = [-2:0.01:2]';
 y1 = 0.5 * x1 .^2;

 
 % draw the ball
 i = [0:0.01:1]' * 2 * pi;
 xb = 0.05*cos(i) + x;
 yb = 0.05*sin(i) + y + 0.05 + 0.03*abs(x);
 
 % line through the ball
 q = [0, pi] - L/0.05;
 xb1 = 0.05*cos(q) + x;
 yb1 = 0.05*sin(q) + y + 0.05 + 0.03*abs(x);
 
 plot(x1,y1,'b', xb, yb, 'r', xb1, yb1, 'r');
 xlim([-2,2]);
 ylim([0,2]);
 pause(0.01);
 end