ball in a cone - Lagrange mechanics

a point mass moves under the influence of gravity on the wall of a circle cone. Equations of motion for the two DOF's r and phi are obtained from the lagrangian L and solved numerically for a certain initial condition:

tspan = [0 T]; % time span for simulation
[r(t=0) r'(t=0) phi(t=0) phi'(t=0) ] initial conditions
y20 = [1.3 0 0 w ]; % w - angular frequency
f = @(l,y2) [y2(2); -g*cos(a) + y2(1)*(y2(4)^2)*((sin(a))^2)-k*(y2(2)^2+y2(4)^2)^0.5;y2(4);(-2*y2(2)*y2(4))/(y2(1))] ;

[l,y2]=ode45(f,tspan,y20); % call ode45 solver

the zip-file contains a mp4-video of the animation (created using matlabs WriteVideo() function)