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Bodies in space

Bodies in space
ARC | Linkage Projects
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  • Using the Geometric Phase to Optimise Planar Somersaults

    Tong, William; Dullin, Holger R. (2018)
    Projects: ARC | Bodies in space (LP100200245)
    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 the second is the geometric phase that is independent of angular momentum and depends solely on the details of the shape change. Next, we import digitised footage of an elite athlete performing 3.5 forward somersaults off the 3m springboard, and use the data to validate our model. We show that reversing and reorderin...

    Twisting Somersault

    Dullin, Holger R.; Tong, William (2015)
    Projects: ARC | Bodies in space (LP100200245)
    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 the twisting motion is apparent in a body frame, while the somersaulting (rotation about the fixed angular momentum vector in space) is recovered by a combination of dynamic and geometric phase. In the simplest "kick-model" the number of somersaults $m$ and the number of twists $n$ are obtained through a rational rot...

    A New Twisting Somersault - 513XD

    Tong, William; Dullin, Holger R. (2016)
    Projects: ARC | Bodies in space (LP100200245)
    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 (513X...

    The Equilateral Pentagon at Zero Angular Momentum: Maximal Rotation Through Optimal Deformation

    Tong, William; Dullin, Holger R. (2011)
    Projects: ARC | Bodies in space (LP100200245)
    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 question of how much the pentagon can rotate with zero angular momentum. We show that the shape space of the equilateral pentagon has genus 4 and find a fundamental region by discrete symmetry reduction with respect to symmetry group D_5. The amount of rotation \Delta \theta for a loop in shape space at zero angular m...

    The Diver with a Rotor

    Bharadwaj, Sudarsh; Duignan, Nathan; Dullin, Holger R.; Leung, Karen; Tong, William (2015)
    Projects: ARC | Bodies in space (LP100200245)
    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 devise explicit analytical formulas whilst still maintaining sufficient complexity to preserve the shape-changing dynamics essential for twisting somersaults in springboard and platform diving. With `rotor on' and with `rotor off' the corresponding Euler-type equations can be solved, and the essential quantities cha...
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