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Angular Momentum in Multiple Rotation Nontwisting Platform Dives

Joseph Hamill, Mark D. Ricard, and Dennis M. Golden

A study was undertaken to investigate the changes in total body angular momentum about a transverse axis through the center of mass that occurred as the rotational requirement in the four categories of nontwisting platform dives was increased. Three skilled subjects were filmed performing dives in the pike position, with increases in rotation in each of the four categories. Angular momentum was calculated from the initiation of the dive until the diver reached the peak of his trajectory after takeoff. In all categories of dives, the constant, flight phase total body angular momentum increased as a function of rotational requirement. Increases in the angular momentum at takeoff due to increases in the rotational requirement ranged from a factor of 3.61 times in the forward category of dives to 1.52 times in the inward category. It was found that the remote contribution of angular momentum contributed from 81 to 89% of the total body angular momentum. The trunk accounted for 80 to 90% of the local contribution. In all categories of dives except the forward 1/2 pike somersault, the remote percent contribution of the arms was the largest of all segments, ranging from 38 to 74% of the total angular momentum.

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Upper Extremity Function in Running. II: Angular Momentum Considerations

Richard N. Hinrichs

Ten male recreational runners were filmed using three-dimensional cinematography while running on a treadmill at 3.8 m/s, 4.5 m/s, and 5.4 m/s. A 14-segment mathematical model was used to examine the contributions of the arms to the total-body angular momentum about three orthogonal axes passing through the body center of mass. The results showed that while the body possessed varying amounts of angular momentum about all three coordinate axes, the arms made a meaningful contribution to only the vertical component (Hz). The arms were found to generate an alternating positive and negative Hz pattern during the running cycle. This tended to cancel out an opposite Hz pattern of the legs. The trunk was found to be an active participant in this balance of angular momentum, the upper trunk rotating back and forth with the arms and, to a lesser extent, the lower trunk with the legs. The result was a relatively small total-body Hz throughout the running cycle. The inverse relationship between upper- and lower-body angular momentum suggests that the arms and upper trunk provide the majority of the angular impulse about the z axis needed to put the legs through their alternating strides in running.

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Greg Louganis’ Springboard Takeoff: II. Linear and Angular Momentum Considerations

Doris I. Miller and Carolyn F. Munro

A linear and angular momentum analysis was conducted on Greg Louganis' forward and reverse 3-m springboard takeoffs performed during National Sports Festival V in Colorado Springs, and differences among dives were examined. At initial contact with the board, his horizontal velocity approximated 0.5 m/s across all dives analyzed. In the forward 3.5 somersaults pike, the horizontal velocity subsequently increased in magnitude until the latter half of recoil. By contrast, in the forward and reverse dives and reverse 2.5 somersaults, horizontal velocity displayed an initial reduction followed by an increase to the final value of 0.8 to 1.2 m/s. His vertical velocities at touchdown (−4.3 to −4.5 m/s) increased to 5.0 to 6.0 m/s during the takeoff, with the final upward velocity being related to the type of dive performed. At initial contact, Louganis’ total body angular momentum with respect to his center of gravity was negligible. By the end of the takeoff, it had increased to 18 kg-m-m/s for the forward dive straight and was three and four times that magnitude for his reverse 2.5 and forward 3.5 somersaults pike, respectively. Between 80 and 90% of the total angular momentum at the end of the takeoff was due to the segment remote contributions. The importance of the upper extremities in developing somersaulting angular momentum was shown by the fact that they were responsible for between 30 and 43% of the final angular momentum in all but the forward dive straight.

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Optimum Technique for Generating Angular Momentum in Accelerated Backward Giant Circles Prior to a Dismount

Michael J. Hiley and M.R. Yeadon

In men’s artistic gymnastics the backward giant circle on the high bar is used to produce the angular momentum that the gymnast needs for executing somersaulting dismounts. Dismounts in which the gymnast performs two somersaults in the layout (straight body) position require the greatest angular momentum. However, it appears there are two distinct techniques that elite gymnasts use when performing backward giant circles prior to a double layout somersault dismount. The “traditional” technique has been superseded by the “scooped” technique which is now used by the majority of elite gymnasts. To determine whether the scooped technique is better at producing angular momentum, a simulation model was used to optimize the angular momentum about the mass center at release. The model was evaluated using data obtained from a force/video analysis of accelerated giant circles. The model was able to estimate the reaction forces measured by strain gauges on the bar to within 9% of the peak forces, and the body rotation angle to within 1% of total rotation. During the optimizations, the joint angle time histories of the model were manipulated in order to maximize the angular momentum about the model’s mass center at release. Two optima were found which were characteristic of the two backward giant circle techniques used by elite gymnasts. The traditional technique produced more angular momentum than the scooped technique, although both were capable of producing sufficient angular momentum for a double layout somersault dismount. This suggests that the preference of elite gymnasts for the scooped technique must be based on factors other than the production of angular momentum.

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Angular Momentum and Performance in the Triple Jump: A Cross-Sectional Analysis

Bing Yu and James G. Hay

The purposes of this study were (a) to determine the magnitude of the angular momentum elite triple jumpers possess during each of the three phases of a triple jump, and (b) to identify those components of the angular momentum that are closely related to the actual distance of the triple jump. Angular momentum about each of three orthogonal axes at the takeoff of each of the last stride, hop, step, and jump was computed from the smoothed 3-D coordinate data of 21 body landmarks and joint centers and normalized to body mass (mb) and standing height (hb). Linear and nonlinear regression analyses were conducted to examine the relationships between angular momenta and actual distance. The results suggested that the estimated optimum magnitude of this side-somersaulting angular momentum is 0.0069 mb hb 2 kg · m2 · s-1 toward the side of the free leg, that the side-somersaulting angular momentum needed at the takeoff of the step should be obtained during the support phase of the hop; and that the change in the side-somersaulting angular momentum during the support phase of the step should be minimized.

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The Gait of Children With and Without Cerebral Palsy: Work, Energy, and Angular Momentum

Shawn Russell, Bradford Bennett, Pradip Sheth, and Mark Abel

This paper describes a method to characterize gait pathologies like cerebral palsy using work, energy, and angular momentum. For a group of 24 children, 16 with spastic diplegic cerebral palsy and 8 typically developed, kinematic data were collected at the subjects self selected comfortable walking speed. From the kinematics, the work—internal, external, and whole body; energy—rotational and relative linear; and the angular momentum were calculated. Our findings suggest that internal work represents 53% and 40% respectively of the whole body work in gait for typically developed children and children with cerebral palsy. Analysis of the angular momentum of the whole body, and other subgroupings of body segments, revealed a relationship between increased angular momentum and increased internal work. This relationship allows one to use angular momentum to assist in determining the kinetics and kinematics of gait which contribute to increased internal work. Thus offering insight to interventions which can be applied to increase the efficiency of bipedal locomotion, by reducing internal work which has no direct contribution to center of mass motion, in both normal and pathologic populations.

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Contributions of Angular Momentum and Catting to the Twist Rotation in High Jumping

Jesús Dapena

This project sought to break down high jump twist rotation into portions contributed by angular momentum and those contributed by rotational action and reaction ("catting"). Five male and 5 female high jumpers were studied with three-dimensional film/video analysis procedures. The hip twist angle at the peak was broken down into an initial twist angle at takeoff and the subsequent twist rotation accumulated between takeoff and the peak. The latter was in turn broken down into rotations contributed by the twisting component of angular momentum and rotations contributed by catting. It was found that the contribution of catting to the twist rotation was at least as large as that of the angular momentum. The important contribution of catting to the twist rotation introduces the possibility that defects in its execution might play a role in the problems that some high jumpers have with twist rotation.

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Effects of the Method of Body Segment Parameter Estimation on Airborne Angular Momentum

Young-Hoo Kwon

Ten body segment parameter (BSP) estimation methods were selected to compute the BSPs of 3 collegiate male gymnasts: cadaver-based methods (Group C, 4 methods), mass scanning-based methods (Group M, 4 methods) and geometric methods (Group G, 2 methods). Angular momenta of nine double somersault with full twist H-bar dismounts performed by the 3 gymnasts were computed. Each trial was processed 10 times using 10 sets of BSPs obtained from the estimation methods. Intergroup and intermethod comparisons of the airborne angular momenta were made. It was concluded that the method of BSP estimation affected the magnitude of airborne angular momentum but did not affect the magnitude of angular momentum fluctuation during the airborne phase.

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Angular Momentum Requirements of the Twisting and Nontwisting Forward 1 1/2 Somersault Dive

Ross H. Sanders and Barry D. Wilson

This study investigated the in-flight rotation of elite 3m springboard divers by determining the angular momentum requirement about the transverse axis through the divers center of gravity (somersault axis) required to perform a forward 1 1/2 somersault with and without twist. Three elite male divers competing in the 1982 Commonwealth Games were filmed using high-speed cinematography while performing the forward 1 1/2 somersault in the pike position and the forward 1 1/2 somersault with one twist in a free position. The film was digitized to provide a kinematic description of each dive. An inclined axis technique appeared to be the predominant means of producing twist after takeoff from the board. The angular momentum about the somersault axis after takeoff was greater for the forward 1 1/2 somersault with twist than the forward 1 1/2 somersault without twist for all three divers. The difference in angular momentum between the two dives of each diver ranged from 6% to 19%. The most observable difference between the dives during the preflight phases was the degree of hip flexion at takeoff. There was more hip flexion at takeoff in 5132D than 103B for all three divers. This difference ranged from 9° to 18° (mean = 14°).

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Initiating Rotation in Back and Reverse Armstand Triple Somersaults Tuck Dives

Karen Murtaugh and Doris I. Miller

To determine strategies for initiating rotation in armstand back and reverse triple somersaults tuck dives from the 10-m platform, videotaped records of 17 elite male divers performing in competitions between 1995 and 1999 were analyzed. Linear and angular momenta at last contact were similar for both dives. Although the lower extremity actions were comparable, they occurred significantly earlier (p < .05) in reverse triple takeoffs, allowing divers to enter the tuck more quickly. As divers lean, the moment arm of the vertical platform reaction force increases with respect to the CG. The vertical platform reaction force moment promotes back and opposes reverse somersaulting angular momentum. Meanwhile, the horizontal platform reaction force moment promotes reverse and opposes back somersaulting angular momentum. Consequently, divers performing reverse triples maintained a more vertical trunk position during the early part of the takeoff, while those executing back triples leaned further before initiating lower and upper extremity actions to exert force against the platform. Since the strategy for reverse rotation may result in the head passing close to the platform and there is very little to gain in degree of difficulty, it is recommended that competitors execute back rather than reverse somersaulting armstand dives.