11 citations · 23 across the 4 of their papers we have counts for
5 papers
Using the Geometric Phase to Optimise Planar Somersaults
William Tong, Holger R. Dullin
We derive the equations of motion for the planar somersault, which consist of two additive terms. The first is the dynamic phase that is proportional to the angular momentum, and t…
A New Twisting Somersault - 513XD
William Tong, Holger R. Dullin
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 genera…
Twisting Somersault
Holger R. Dullin, William Tong
A complete description of twisting somersaults is given using a reduction to a time-dependent Euler equation for non-rigid body dynamics. The central idea is that after reduction t…
The Diver with a Rotor
Sudarsh Bharadwaj, Nathan Duignan, Holger R. Dullin +2
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…
The Equilateral Pentagon at Zero Angular Momentum: Maximal Rotation Through Optimal Deformation
William Tong, Holger R. Dullin
A pentagon in the plane with fixed side-lengths has a two-dimensional shape space. Considering the pentagon as a mechanical system with point masses at the corners we answer the qu…