The diver with a rotor

We present and analyse a simple model for the twisting somersault. The model consists of a rigid body with a rotor attached that can be switched on and off. This makes it simple enough to devise explicit analytical formulas whilst still maintaining sufficient complexity to preserve the shape-changing dynamics essential for twisting somersaults performed in springboard and platform diving. With “rotor on” and with “rotor off” the corresponding Euler-type equations can be solved and the essential quantities characterising the dynamics, such as the periods and rotation numbers, can be computed in terms of complete elliptic integrals. We arrive at explicit formulas for how to achieve a dive with m somersaults and n twists in a given total time. This can be thought of as a special case of a geometric phase formula due to Cabrera (2007).