% This is the suitcase problem from Suherman, et al., Effect of Human
% Response Time on Rocking Instability of a Two-Wheeled Suitcase,
% J. of Sound and Vibration, Vol. 207 (5), 1997, 617-625. Event
% location is used to find when the wheels impact the ground and
% when the suitcase has fallen over. The parameter values are those
% used to generate Figure 3a in the reference.

state = +1;
opts = ddeset('RelTol',1e-5,'AbsTol',1e-5,'Events','exam8e');
sol = dde23('exam8f',0.1,[0; 0],[0 12],opts,state);

% Reference values for event locations:
ref = [4.516757065, 9.751053145, 11.670393497];
fprintf('\nKind of Event:                 dde23   reference\n');
event = 0;
while sol.x(end) < 12
   event = event + 1;
   if sol.ie(end) == 1
      fprintf('A wheel hit the ground.   %10.4f  %10.6f\n',...
              sol.x(end),ref(event));
      state = - state;
      opts = ddeset(opts,'InitialY',[ 0; 0.913*sol.y(2,end)]);
      sol = dde23('exam8f',0.1,sol,[sol.x(end) 12],opts,state);
   else     
      fprintf('The suitcase fell over.   %10.4f  %10.6f\n',...
              sol.x(end),ref(event));
      break;
   end
end
plot(sol.y(1,:),sol.y(2,:))
title('Figure 8.  Suitcase problem.')
xlabel('\theta(t)')
ylabel('\theta''(t)')