The pilot rented the special light sport airplane from a fixed base operator for the purpose of conducting a personal flight to a non-towered airport, where he planned to practice landings and takeoffs. He entered a left traffic pattern for runway 11 at the destination airport, and conducted a normal touch-and-go landing and takeoff, with the intent of conducting at least one more touch-and-go on the same runway. He used the same flap and power settings for the second approach, but noted that the second approach was "slightly shallower than normal." After touchdown, the airplane bounced. The pilot maintained the pitch attitude, and the airplane touched down and bounced again. He then added power with the intent to abandon the landing, but the propeller struck the runway. The pilot reduced power and the airplane slid to a stop on the runway. The nose landing gear was collapsed aft, and penetrated the fuselage fuel tank, which resulted in substantial damage. The pilot reported no preimpact mechanical malfunctions or failures with the airplane that would have precluded normal operation.