A new twisting somersault


William Tong, Holger R. Dullin*

*Corresponding author for this work

Research output: Contribution to journalArticle

1 Citation (Scopus)


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.

Original languageEnglish
Pages (from-to)2037–2061
Number of pages25
JournalJournal of Nonlinear Science
Issue number6
Publication statusPublished - Dec 2017
Externally publishedYes


  • Biomechanics
  • Geometric phase
  • Nonrigid body dynamics
  • Twisting somersault

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