The flight instructor in the helicopter reported that, she provided takeoff and landing training from and to, a helicopter landing platform. During landing, the student pilot had control of the collective and the anti-torque pedals, and the flight instructor had maintained control of the cyclic. The flight instructor asserted that during landing to the platform, "the student lowered the collective suddenly, and also pulled back up (on the collective) suddenly as well." Additionally, the student grabbed the cyclic and pulled aft, when he increased the collective. The helicopter bounced on the platform and "tilted backwards." The helicopter started to roll to its right side, and the instructor closed the throttle. The helicopter rolled onto its right side and the main rotor blades struck the ground. The helicopter sustained substantial damage to the main and tail rotor drive systems and the fuselage. The pilot reported that there were no preaccident mechanical failures or malfunctions with the helicopter that would have precluded normal operation.