% Dynamics of a ball rolling in a bowl where
%    y = 1/2 x^2
%

x = 1.5;
dx = 0;
dt = 0.01;
t = 0;
while(t < 100)
    
% compute the acceleration

ddx = -( 1.4*dx*dx + 9.8) * x / ( 1.4*(1 + x*x) );

% integrate

dx = dx + ddx*dt;
x = x + dx*dt;

% display the ball
 y = 0.5*x*x;

 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) + 0.5*x^2 + 0.05 + 0.02*abs(x);
 
 % line through the ball
 q = [0, pi] - x/0.05;
 xb1 = 0.05*cos(q) + x;
 yb1 = 0.05*sin(q) + 0.5*x^2 + 0.05 + 0.02*abs(x);
 
 plot(x1,y1,'b', xb, yb, 'r', xb1, yb1, 'r');

 pause(0.01);
 end