Coupled Rigid Body Dynamics with Application to Diving

Platform and springboard diving is a sport involving athletes falling or jumping into a pool of water, usually while performing acrobatic manoeuvres. At the highest level it challenges the physical laws of gravity as athletes try to outperform each other by executing more sophisticated dives. With a mathematical model we are able to assist the athletes and coaches by providing some insight into the mechanics of diving, which hopefully gives them an edge during competition. In this thesis we begin with an introduction to rigid body dynamics and then extend the results to coupled rigid bodies. We generalise Euler's equations of motion and equations of orientation for rigid bodies to be applicable for coupled rigid bodies. The athlete is represented as a mathematical model consisting of ten simple geometric solids, which is used to conduct three projects within this thesis. In the first project we look at somersaults without twists, which provides a significant reduction as the model becomes planar. The equations of motion and equations of orientation reduce from vector form to a single scalar differential equation for orientation, since angular momentum is conserved. We digitise footage of an elite diver performing 107B (forward 3.5 somersault in pike) from the 3m springboard, and feed that data into our model for comparison between the theoretically predicted and observed result. We show that the overall rotation obtained by the athlete through somersault is composed of two parts, the major contribution coming from the dynamic phase and a small portion from the geometric phase. We note that by modifying the digitised dive slightly we can leave the dynamic phase intact, but change the geometric phase to provide a small boost in overall rotation. The technique involved in doing so is not practical for actual diving though, so we move away from this idea and devise another way of optimising for the overall rotation. We find that by shape changing in a particular way that takes slightly longer than the fastest way of moving into and out of pike, the overall rotation achieved can be improved by utilising the geometric phase. In the second project we use the model to simulate divers performing forward m somersaults with n twists. The formulas derived are general, but we will specifically look at 5132D, 5134D, 5136D, and 5138D (forward 1.5 somersaults with 1, 2, 3, and 4 twists) dives. To keep the simulation as simple as possible we reduce the segment count to two by restricting the athlete to only using their left arm about the abduction-adduction plane of motion. We show how twisting somersaults can be achieved in this manner using this simple model with predetermined set of motor actions. The dive mechanics consist of the athlete taking off in pure somersaulting motion, executing a shape change mid-flight to get into twist position, perform twisting somersaults in rigid body motion, and then executing another shape change to revert the motion back into pure somersaulting motion to complete the dive. In the third and final project we use our model to show how a 513XD dive (forward 1.5 somersaults with 5 twists) is performed. This complicated dive differs from all currently performed dives in that once the diver initiates twist in the somersaulting motion via shape change, they need to perform another appropriately timed shape change to speed up the twist rather than stopping the twist, and only then is five twists obtainable with practical parameters. Such techniques can be found in aerial skiing where the airborne time is longer, but our theory shows that it may also be applicable to platform and springboard diving too. To date, no athlete has ever attempted a 513XD in competition, nor does the International Swimming Federation (FINA) cover dives with five twists in their degree-of-difficulty formula. Our theory shows that 513XD dive is theoretically possible, and with extrapolation we estimate it would have a degree-of-difficulty of 3.9

New laser spectroscopic technique for stable-isotope ratio analysis

Reliable and safe application of isotopes as tracers is important in many areas, including biomedical, environmental and geochrono- logical sciences. A new approach to stable-isotope ratio analysis based on atomic hyperfine structure is demonstrated. This laser spectroscopic scheme is virtually interference-free because of the highly selective and specific nature of hyperfine structures. Hence, a minor constituent in a complex matrix can be selectively analyzed without extensive sample preparation. A single-frequency tunable cw ring dye laser is used as the excitation source and a specially designed and constructed demountable cathode discharge is used as the atomizer and detector. Samples are electrodeposited on the demountable cathode and hyperfine profiles are collected by optogalvanic detection. By spectral deconvolution, the relative abundances of all isotopes present can be determined with good accuracy and precision. The technique is demonstrated for copper concentrations as low as 1.6 ppm, using the atomic hyperfine structure of Cu I 578.2 nm non-resonance transition. It is also successfully tested for analysis of copper isotopes in human blood;The sensitivity of Doppler-free polarization spectroscopy in atomic flames is demonstrated to be competitive with other sensitive laser techniques such as the fluorescence spectrometric methods. Improved detectability of polarization rotation and excellent suppression of flame background noise enable this method to achieve detection limits of parts per trillion levels of sodium and 37 ppb of barium, while taking advantage of the convenient sample introduction of analytical flames. Furthermore, since polarization spectroscopy provides Doppler-free information, the spectral;resolution is suitable for isotopic analysis, and the technique offers excellent selectivity and minimum spectral interference; (\u271)DOE Report IS-T-1156. This work was performed under contract No. W-7405-Eng-82 with the U.S. Department of Energy

The Diver with a Rotor

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 characterising the dynamics, such as the periods and rotation numbers, can be computed in terms of complete elliptic integrals. Thus we arrive at explicit formulas for how to achieve a dive with m somersaults and n twists in a given total time. This can be thought of as a special case of a geometric phase formula due to Cabrera 2007.Comment: 15 pages, 6 figure

Painting Analysis Using Wavelets and Probabilistic Topic Models

In this paper, computer-based techniques for stylistic analysis of paintings are applied to the five panels of the 14th century Peruzzi Altarpiece by Giotto di Bondone. Features are extracted by combining a dual-tree complex wavelet transform with a hidden Markov tree (HMT) model. Hierarchical clustering is used to identify stylistic keywords in image patches, and keyword frequencies are calculated for sub-images that each contains many patches. A generative hierarchical Bayesian model learns stylistic patterns of keywords; these patterns are then used to characterize the styles of the sub-images; this in turn, permits to discriminate between paintings. Results suggest that such unsupervised probabilistic topic models can be useful to distill characteristic elements of style.Comment: 5 pages, 4 figures, ICIP 201

From Lexical Tone to Lexical Stress: A Cross-Language Mediation Model for Cantonese Children Learning English as a Second Language

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Better than native: Tone language experience enhances English lexical stress discrimination in Cantonese-English bilingual listeners

Available online 13 April 2019While many second language (L2) listeners are known to struggle when discriminating non-native features absent in their first language (L1), no study has reported that L2 listeners perform better than native listeners in this regard. The present study tested whether Cantonese-English bilinguals were better in discriminating English lexical stress in individual words or pseudowords than native English listeners, even though lexical stress is absent in Cantonese. In experiments manipulating acoustic, phonotactic, and lexical cues, Cantonese-English bilingual adults exhibited superior performance in discriminating English lexical stress than native English listeners across all phonotactic/lexical conditions when the fundamental frequency (f0) cue to lexical stress was present. The findings underscore the facilitative effect of Cantonese tone language experience on English lexical stress discrimination.This article is, in part, based on the fourth chapter of the PhD thesis submitted by William Choi to The University of Hong Kong. This research was supported, in part, by the Language Learning Dissertation Grant from Language Learning to William Choi. It was also supported by the Pilot Scheme on International Experiences for Research Postgraduate Students from The University of Hong Kong to William Choi, and the Early Career Scheme (27402514), General Research Fund (17673216), and General Research Fund (17609518) from the HKSAR Research Grant Council to Xiuli Tong. Support was also provided by Ministerio de Ciencia E Innovacion, Grant PSI2014-53277, Centro de Excelencia Severo Ochoa, Grant SEV-2015-0490, and by the National Science Foundation under Grant IBSS-1519908 to Arthur Samuel. We thank Benjamin Munson for his useful suggestion about the syllable-timed nature of Cantonese and the four anonymous reviewers for comments that have helped us to develop our ideas and presentation more clearly

An Assessment of NASA Aeropropulsion Technologies: A System Study

Aviation industry s robust growth rate has given rise to growing concerns about the contribution that aviation emissions will make to local air quality and global climate change. Over the last several years, NASA has been engaged in the development of aeropropulsion technologies with specific objectives to reduce aircraft emissions. A system analysis was performed to evaluate the potential impact of these propulsion technologies on aircraft CO2 (directly proportional to fuel burn) and NOx reductions. A large subsonic aircraft, with two 396-kN thrust (85,000-pound) engines was chosen for the study. Performance benefit estimates are presented for each technology, with a summary of potential emissions reduction possible from the development of these technologies. The results show that NASA s aeropropulsion technologies have the potential to significantly reduce the CO2 and NO(x) emissions. The results are used to support informed decision-making on the development of aeropropulsion technology portfolio for CO2 and NO(x) reductions