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We derive the equations of motion for the planar somersault, which consist oftwo additive terms. The first is the dynamic phase that is proportional to theangular momentum, and the second is the geometric phase that is independent ofangular momentum and depends solely on the details of the shape change. Next,we import digitised footage of an elite athlete performing 3.5 forwardsomersaults off the 3m springboard, and use the data to validate our model. Weshow that reversing and reordering certain sections of the digitised dive canmaximise the geometric phase without affecting the dynamic phase, therebyincreasing the overall rotation achieved. Finally, we propose a theoreticalplanar somersault consisting of four shape changing states, where theoptimisation lies in finding the shape change strategy that maximises theoverall rotation of the dive. This is achieved by balancing the rotationalcontributions from the dynamic and geometric phases, in which we show thegeometric phase plays a small but important role in the optimisation process.

Using the Geometric Phase to Optimise Planar Somersaults