2 research outputs found
The Diver with a Rotor
We present and analyse a simple model for the twisting somersault. The model
is a rigid body with a rotor attached which 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 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. Thus 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.Comment: 15 pages, 6 figure