function [ J ] = cost_chain( z )
 % [Z,e] = fminsearch('cost_chain', -5*rand(5,1))
 % ECE 463 Lecture #23: Calculus of Variations
 % Shape of a hanging chain that's 12 meters long
 
   Y = [0,z(1),z(2),z(3),z(4),z(5),z(4),z(3),z(2),z(1),0]';
   PE = sum(Y);
   L = 0;
   for i=2:11
       L = L + sqrt(1 + (Y(i) - Y(i-1))^2);
   end
   E = 12-L;
   J = PE + 1000*E*E;
   plot([0:10]', Y, '.-');
   ylim([-5,1]);
   pause(0.01);
end