A New Twisting Somersault: 513XD

Tong, William M.; Dullin, Holger R.

doi:10.1007/s00332-017-9403-4

Cited by 8 publications

(14 citation statements)

References 16 publications

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“…Currently the forward 1½ with quintuple twist has not been attempted in competition and has not been assigned a degree of difficulty. A previous suggestion as to how the dive might be accomplished (Tong & Dullin, 2016) is unrealistic due to the speed required for the arm movements. The current maximum number of twists in a forward 1½ somersault twisting dive performed in competition from the three metre springboard is four twists (FINA, 2017, Appendix 2).…”

Section: Discussionmentioning

confidence: 99%

The limits of aerial techniques for producing twist in forward 1½ somersault dives

Yeadon

Hiley

2018

Human Movement Science

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An angle-driven computer simulation model of aerial movement was used to determine the maximum amount of twist that can be produced in a forward 1½ somersault dive from a three-metre springboard using various aerial twisting techniques. The segmental inertia parameters of an elite springboard diver were used in the simulations and lower bounds were placed on the durations of arm and hip angle changes based on recorded performances of twisting somersaults. A limiting dive was identified as that producing the largest possible whole number of twists. Simulations of the limiting dives were found using simulated annealing optimisation to produce the required amounts of somersault, tilt and twist after a flight time of 1.5 s. Additional optimisations were then run to seek solutions with the arms less adducted during the twisting phase. It was found that the upper limits ranged from two to five twists with arm abduction ranges lying between 6° and 17°. Similar results were obtained when the inertia parameters of two other springboard divers were used.

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Section: Discussionmentioning

confidence: 99%

The limits of aerial techniques for producing twist in forward 1½ somersault dives

Yeadon

Hiley

2018

Human Movement Science

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“…This coinciding form of solution was repeatedly reproduced in the scientific and educational literature. In particular, following the works of [10,11], the solution can be represented in the following form:…”

Section: Solutions Of the Dynamic Euler-poinsot Equations For Motion mentioning

confidence: 99%

Illustrations of rigid body motion along a separatrix in the case of Euler-Poinsot

Adlaj¹,

Berestova

Misyura

et al. 2018

CTE

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The aim of our paper is to explain a computer animation of the strictly critical rigid body motion, which ought not be confused with any other motion in its "proximity", however close. We demonstrate that the (local) "uniqueness theorem" remarkably fails in the case of critical motion which (time) domain must be compactified via adjoining the point at (complex) infinity. Two (opposite to each other) "flips" correspond to one and the same (initial) rotation, exclusively either clockwise or counterclockwise, (strictly) about the intermediate axis of inertia. These two symmetrical reversals of the direction of the intermediate axis (of inertia), initially matching then opposing the direction of the (fixed) angular momentum, share one and the same (symmetry) axis, which we call "Galois axis". The Galois axis, which is fixed within the body (but coincides with no principal axis of inertia), rotates uniformly in a plane orthogonal to the angular momentum, as our animation demonstrates. The animation also traces the corresponding two (recurrently selfintersecting) herpolhodes, which turn out to be mirror-symmetrical. The "mirror" is exhibited to lie in a plane, orthogonal to Galois axis at the midst of the "flip". The Galois axis itself is reflected across the minor (or the major) axis of inertia if the direction of the angular momentum is reversed. The formula for the "swing" of the intermediate axis in the plane orthogonal to Galois axis (in body's frame), turns out to be "a square root" of Abrarov's critical solution for a simple pendulum, which (imaginary) period is (exactly) calculated.

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“…When optimising θ in (19) for a typical planar somersault with L = 120, we see in Figure 13c that {s in , s out } = {1, 0.8593} yields the maximal rotation, whose shape change trajectory is illustrated in Figure 14. When compared to the dive with {s in , s out } = {1, 1}, the gain in overall rotation is 0.0189 radians or 1.0836 • .…”

Section: Optimising Planar Somersaultsmentioning

confidence: 99%

“…[2,10,13,15], but here we take a different approach that utilises the geometric phase in order to maximise somersault rotation. The geometric phase is also important in the twisting somersault, see [3], and has been used to generate a new dive in [19]. The main focus for the twisting somersault is the generation of twist, while in the planar case the particulars of the shape change can instead be used to generate additional somersault.…”

Section: Introductionmentioning

confidence: 99%

Using the geometric phase to optimize planar somersaults

Tong

Dullin

2018

IMA Journal of Applied Mathematics

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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 reordering certain sections of the digitised dive can maximise the geometric phase without affecting the dynamic phase, thereby increasing the overall rotation achieved. Finally, we propose a theoretical planar somersault consisting of four shape changing states, where the optimisation lies in finding the shape change strategy that maximises the overall rotation of the dive. This is achieved by balancing the rotational contributions from the dynamic and geometric phases, in which we show the geometric phase plays a small but important role in the optimisation process. arXiv:1801.07828v1 [physics.class-ph]

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A New Twisting Somersault: 513XD

Cited by 8 publications

References 16 publications

The limits of aerial techniques for producing twist in forward 1½ somersault dives

The limits of aerial techniques for producing twist in forward 1½ somersault dives

Illustrations of rigid body motion along a separatrix in the case of Euler-Poinsot

Using the geometric phase to optimize planar somersaults

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