A New Twisting Somersault - 513XD

TL;DR

This paper develops a mathematical model of an athlete as a system of coupled rigid bodies to design and analyze a new diving move, 513XD, involving complex twists and somersaults, with potential applications beyond sports.

Contribution

It generalizes Euler's equations to non-rigid bodies and introduces a novel dive sequence with realistic shape changes, demonstrating conversion between somersaulting and twisting motions.

Findings

Designed a new dive sequence 513XD with 1.5 somersaults and 5 twists.

Showed how impulsive shape changes can convert pure somersaults into pure twists.

Provided analytical solutions for simplified shape change scenarios.

Abstract

We present the mathematical framework of an athlete modelled as a system of coupled rigid bodies to simulate platform and springboard diving. Euler's equations of motion are generalised to non-rigid bodies, and are then used to innovate a new dive sequence that in principle can be performed by real world athletes. We begin by assuming shape changes are instantaneous so that the equations of motion simplify enough to be solved analytically, and then use this insight to present a new dive (513XD) consisting of 1.5 somersaults and 5 twists using realistic shape changes. Finally, we demonstrate the phenomenon of converting pure somersaulting motion into pure twisting motion by using a sequence of impulsive shape changes, which may have applications in other fields such as space aeronautics.