On July 8, 2000, about 1320 Eastern Daylight Time, a Cessna 182S, N729AD, was substantially damaged while landing at the Westchester County Airport (HPN), White Plains, New York. The certificated student pilot (SP) was not injured. Visual meteorological conditions prevailed and no flight plan had been filed for the local training flight conducted under 14 CFR Part 91. The airplane was landing on Runway 34, a 6,548 foot long, 150 foot wide, asphalt runway. According to the SP, the airplane landed "flat" and "porpoised." She added engine power; however, she was not able to stop the bouncing. The airplane porpoised three times, and the nose gear was pushed up and back, into the engine firewall. The SP stated she did not have any mechanical problems with the airplane. Winds reported at HPN, at 1345, were from 350 degrees at 9 knots. The SP reported 125 hours of total flight experience, of which, 90 hours were in make and model. The Federal Aviation Administration Airplane Flying Handbook, FAA-H-8083-3, Chapter 8, "Faulty Approaches and Landings," stated in part: "In a bounced landing that is improperly recovered, the airplane comes in nose first setting off a series of motions that imitate the jumps and dives of a porpoise-hence the name...When a porpoise is severe, the safest procedure is to EXECUTE A GO-AROUND IMMEDIATELY. No attempt to salvage the landing should be made...."