Journal of Nonlinear Science

, Volume 27, Issue 6, pp 2037–2061 | Cite as

A New Twisting Somersault: 513XD

Article
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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 that 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 five 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.

Keywords

Nonrigid body dynamics Geometric phase Biomechanics Twisting somersault 

Mathematics Subject Classification

70E55 70E17 37J35 92C10 

Supplementary material

332_2017_9403_MOESM1_ESM.mp4 (442 kb)
Supplementary material 1 (mp4 441 KB)

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsThe University of SydneySydneyAustralia

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