We give a dynamical system analysis of the twisting somersaults using a reduction to a time-dependent Euler equation for nonrigid body dynamics. The central idea is that after reductionthe twisting motion is apparent in a body frame, while the somersaulting (rotation about the fixedangular momentum vector in space) is recovered by a combination of dynamic phase and geometricphase. In the simplest "kick-model" the number of somersaultsmand the number of twistsnareobtained through a rational rotation numberW=m/nof a (rigid) Euler top. Using the full modelwith shape changes that take a realistic time we then derive the master twisting-somersault formula:an exact formula that relates the airborne time of the diver, the time spent in various stages of thedive, the numbersmandn, the energy in the stages, and the angular momentum by extending ageometric phase formula due to Cabrera [J. Geom. Phys., 57 (2007), pp. 1405-1420]. Numericalsimulations for various dives agree perfectly with this formula where realistic parameters are takenfrom actual observations.
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