singularity??? spherical pendulum has no singularity

I try it in "Wolfram Mathematica" and there is no singularity

http://mathematica.stackexchange.com/a/111724/30288

@tomleslie equation is correct see here  http://www.maths.surrey.ac.uk/explore/michaelspages/documentation/Spherical page 3.

@tomleslie  sorry, first system is correct.

{((D@@2)(phi))(t) = -2*(D(phi))(t)*(D(theta))(t)*cos(theta(t))/sin(phi(t)),
            ((D@@2)(theta))(t) = (D(phi))(t)^2*cos(theta(t))*sin(theta(t))-9.8*sin(theta(t))}

see here, http://www.maths.surrey.ac.uk/explore/michaelspages/documentation/Spherical  (gape 3.)