Dr William Tong

Email: william.tong@mq.edu.au

I was a doctoral student and Postgraduate Teaching Fellow in the School of Mathematics and Statistics at the University of Sydney, and am now a Post-Doctoral Research Fellow in Health Analytics at the Australian Insistute of Health Innovation (AIHI), Macquarie University. I obtained a major in applied mathematics and a minor in IT for my undergraduate studies. In Honours, I modelled a shape changing equilateral pentagon to investigate the phenomenon of rotating at zero angular momentum. Through my research I determined the optimum shape change strategy that maximises the overall rotation obtained after a cycle of deformations.

My PhD thesis was in coupled rigid body dynamics with application to diving, in which I applied and extended methods from the field of geometric mechanics to analyse platform and springboard diving. My project involved examining the dynamics of a rigid body and extending it to a system of coupled rigid bodies. Modelling the diver as a coupled rigid body system, I generalised Euler's equations of motion for rigid bodies and used the differential equations to optimise and simulate pure and twisting somersaults. A defining achievement of my project was the discovery of a new dive sequence that in principle can be performed by real world athletes, which will revolutionise the sport of diving if successfully performed in competition. Some notable mentions of my work include:

Pentagon Research

Genus 4
This is topologically equivalent to the shape space of the equilateral pentagon.
The Equilateral Pentagon at Zero Angular Momentum: Maximal Rotation Through Optimal Deformation - arXiv | local

Interactive Media

You can download the free Wolfram CDF player here.
Animation of shape change along optimal loops - download
Manipulate function to explore shape space - download


Alternatively, you can save the corresponding .mov files.
Optimal loop around the regular convex pentagon - download
Optimal loop around the pentagram - download
Optimal loop around the subset of all equilateral convex pentagons - download

Diving Research

The Athlete
The athlete - comprised of appropiately connected simple geometric solids.
Doctorate thesis - download


1) The Diver with A Rotor - arXiv | ResearchGate
2) Twisting Somersault - arXiv | ResearchGate
3) A new Twisting Somersault - 513XD - arXiv | ResearchGate


Geometric Phase in Diving


1.5 somersaults with 3 twists [5136D] - download
1.5 somersaults with 5 twists [513XD] - download
Orbit comparison between 2 twisting somersaults - download
Wobbling somersault - download

Last updated on 06/06/2017