The student pilot reported that during the takeoff ground roll on the runway, about 35 knots, the pilot moved the control stick slightly forward from the aft position and allowed the nose wheel to rise slightly above the surface, while he increased the throttle setting to 75%. As the gyroplane reached about 70 knots, it started to veer to the left and shudder, so the pilot slightly decreased the throttle setting. As the pilot approached the end of the runway, the pilot increased the throttle setting and maintained the control stick position. Subsequently, the gyroplane pitched up and rolled onto its right side. The gyroplane impacted the ground and slid to a stop on its right side within the runway safety area. The gyroplane sustained substantial damage to the drivetrain. The pilot reported that there were no preaccident mechanical failures or malfunctions with the gyroplane that would have precluded normal operation. The pilot added that during the takeoff, he should have held the aft position of the control stick to maintain the rotor RPM or aborted the takeoff earlier.