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A single-rigid-body model is used to approximately calculate total triple jump distance and phase ratios, given phase takeoff angles and last stride takeoff velocity. Each of the three phases contains two segments: support from touchdown to takeoff, and gravitational flight with air drag. Translational and rotational equations of motion including track reaction forces and moments describe center-of-mass translation and rotation during support segments. In each support, human muscular inputs shape the track reaction force. Two very simple assumptions are made about the orientation of the body during flight, namely that the body remains vertical and takes off with zero pitching angular momentum. Evaluation of the vertical and horizontal support impulses reveals takeoff angles as control variables and that the essential optimization problem can be viewed as choosing sequentially three takeoff angles to maximize total distance. To assess validity, numerical results are compared with actual competition measurements.

An approximate single-rigid-body (SRB) model for triple jump (Okubo and Hubbard, 2025) is used numerically to investigate total distance in terms of run-up speed and hop, step and jump takeoff angles. At each speed a single optimal combination of takeoff angles produces maximum total distance. Using the model with previously measured realistic elite takeoff angles confirms roughly linear correlation between loss of horizontal velocity and gain in vertical velocity during support. It is striking that the simple assumptions in the SRB model (regarding body orientation and lack of pitching angular velocity in flight) are able to account, even loosely, for the velocity conversion process, Yu and Hay, (1996). As total distance increases, the likelihood of a jump-dominated optimal strategy also increases with these features: horizontal speed is maintained in hop and step; jump and step takeoff angles are the largest and smallest, respectively, of the three; step distance is shortest. In the speed range 10.0–10.5 m/s the optimum jump-dominated technique is always best, but only marginally (almost too marginally to notice). The model evaluates importance of run-up speed which mostly affects takeoff speeds, but has almost no effect on optimal takeoff angles. Although the model is deterministic, it can be used with random initial conditions to understand uncertainty effects in jumper execution. Use of the model shows that phase ratios are not controllable parameters but only results.

The objective of this study was to explore the interrelationships between key variables of takeoff technique among long jumpers of various performance levels. Attempts of thirty-seven male athletes were filmed with a video camera, operating at 240 Hz, during their competitive performances in long jumps and analysed using 2D video analysis (SkillSpector software was used). The characteristics of takeoff movements of athletes who had effective distance from the first (7.54 m) to eighteenth (6.76 m) and from the nineteenth (6.74 m) to thirty-seventh (4.93 m) were compared. Correlation and multiple regression analysis were used to evaluate the interdependence between the characteristics of takeoff technique in long jump. It was found that jumpers of higher performance level had significantly larger takeoff velocity of the center of gravity (8.73 ± 0.43 and 8.24 ± 0.47 m.s-1, respectively), its horizontal (8.00 ± 0.41 and 7.68 ± 0.45 m.s-1) and vertical (3.48 ± 0.38 and 2.95 ± 0.43 m.s-1) components, and takeoff angle (23.5 ± 2.3 and 20.6 ± 2.5°). Also, they performed takeoff significantly faster (ground contact time 0.129 ± 0.009 and 0.140 ± 0.014 s, respectively). Only one strong or medium correlation was exhibited between the effective distance and kinematic takeoff characteristics in both groups of athletes (r = 0.71 between effective distance and knee angle at touchdown in the less qualified group). Multiple regression analysis identified knee angle at touchdown and takeoff velocity as key variables of long jump for less qualified jumpers.

The objective of this study was to explore the interrelationships between key variables of takeoff technique among long jumpers of various performance levels. Attempts of thirty-seven male athletes were filmed with a video camera, operating at 240 Hz, during their competitive performances in long jumps and analysed using 2D video analysis (SkillSpector software was used). The characteristics of takeoff movements of athletes who had effective distance from the first (7.54 m) to eighteenth (6.76 m) and from the nineteenth (6.74 m) to thirtyseventh (4.93 m) were compared. Correlation and multiple regression analysis were used to evaluate the interdependence between the characteristics of takeoff technique in long jump. It was found that jumpers of higher performance level had significantly larger takeoff velocity of the center of gravity (8.73 ± 0.43 and 8.24 ± 0.47 m-s-1, respectively), its horizontal (8.00 ± 0.41 and 7.68 ± 0.45 m-s-1) and vertical (3.48 ± 0.38 and 2.95 ± 0.43 m-s-1) components, and takeoff angle (23.5 ± 2.3 and 20.6 ± 2.5°). Also, they performed takeoff significantly faster (ground contact time 0.129 ± 0.009 and 0.140 ± 0.014 s, respectively). Only one strong or medium correlation was exhibited between the effective distance and kinematic takeoff characteristics in both groups of athletes (r = 0.71 between effective distance and knee angle at touchdown in the less qualified group). Multiple regression analysis identified knee angle at touchdown and takeoff velocity as key variables of long jump for less qualified jumpers.

In order to comply with the existing standard requirements or specifications, a new computational method for aircraft take-off and landing performance, which deals with the characteristics of the high precision of parameters in the process of take-off and landing based on flight simulation technique. The simulation model for a twin-engine normal layout aircraft is constructed in detail, including nonlinear motion equation, aerodynamic, engine, landing gear and dynamical mass model. According to performance calculation standard and pilot control specification for different take-off modes and landing stages, the simulation process for one engine inoperative(OEI) take-off, angle of attack(AoA) hold take-off, standard take-off, reject take-off and landing are designed, and corresponding performance computer software is developed to achieve the goal of accuracy as well as full parameters calculation. Compared with the existing methods, the computational complexity of this method is increased, the process is detailed, the parameters are increased, and more influencing factors can be analyzed quantitatively. Results show that OEI take-off distance is the longest, standard take-off is suitable for light aircraft, angle of attack hold take-off is appropriate in plateau or limited thrust. Landing distance is related to glide angle. Therefore, light aircraft landing can reduce the approach speed and increase the glide angle. 为使飞机起降性能计算满足现有飞行性能计算标准或规范，针对起降过程涉及影响因素多、参数精度要求高的特点，提出了基于飞行仿真技术对不同起飞方式和着陆阶段仿真计算起降性能的方法。详细地建立了双发正常式布局飞机各分系统对应模型，包括非线性运动方程、气动力、发动机、起落架、动态质量模型。根据不同起飞方式和着陆阶段的性能计算标准及驾驶员操纵规范设计了单发起飞、两点式起飞、三点式起飞、中断起飞和着陆性能仿真计算流程，并开发相应的程序完成了该过程中全部参数的计算。较现有方法计算复杂性增加，过程详细，可计算的参数增多，能对各类影响因素进行量化分析。结果表明单发起飞距离最长，轻型飞机宜采取三点式起飞，当飞机在高原或推力受限时宜采取两点式起飞；着陆距离与下滑轨迹角相关，轻型飞机着陆可以降低进场速度、增加下滑角。

The application of X-ray photoelectron spectroscopy (XPS) for studies of surface layers of objects with spherical shape was investigated using as examples polystyrene and poly(styrene-acrolein) microspheres with attached human serum albumin (HSA). The amounts of immobilized protein were determined by the standard biochemical Lowry method and by XPS, using the intensity of the N1s signals of HSA as a basis for evaluation. The XPS data were treated by taking into account the spherical shape of the particles analyzed (variable take-off angle of ejected electrons). The best agreement between the results of the biochemical and XPS determinations was found assuming that for the average particle the takeoff angle varies from 0° to 72.7°. This reflects the fact that in the multilayer arrangement of particles, placed onto the support of the XPS apparatus, the particles from the upper layer partially screen the edges of the particles in the layer below.[PUBLICATION ABSTRACT]

Experiment 19.1: Measurement of X-Ray Intensities. Figures A19.1 through A19.3 show EDS spectra from the NiCrAl specimen at 10, 15, and 30 kV, respectively. The take-off angle is 42.0° with the specimen tilted at 30.0° and the x-ray detector at a 12.0° takeoff angle (when the specimen tilt was 0°).

Current methods for converting Euler angles to a rotation quaternion are computationally intensive and have limited practical applications in aerospace. This study introduces an efficient approach that directly converts Euler angles in any desired sequence to a rotation quaternion, eliminating the need for intermediate Euler angle transformation matrices, which leads to a significant improvement in computational efficiency. Moreover, it is general because it works with all 12 possible sequences of rotations. A case study is presented, demonstrating the application of the algorithm in converting between the launch frame and the missile frame of a vertical takeoff vertical landing (VTVL) rocket. The results show more than a ninefold improvement in computational efficiency compared to the classical Euler angle method while maintaining consistency of results.

Ski-jump takeoff of carrier-based aircraft is a very risky subject. At present, the principle, characteristics and influencing factors of ski-jump takeoff are mainly studied at home and abroad, but there is no relevant research on how to carry out ski-jump takeoff test and related risk control. To ensure smooth and safe ski-jump takeoff testing, this paper first determines the influencing factors of ski-jump takeoff based on the dynamics model. Secondly, based on the BP neural network, the corresponding relationship between the influencing factors, the angle of attack and the lifting speed is established. Finally, the quantitative analysis conclusion of the influencing factors is obtained according to the multi-factor weight analysis method and put forward the design method takeoff under the combined conditions of “weight-center of gravity-inertia-configuration” and the test risk control measures, which provides methods and ideas for the safety of ski-jump takeoff test.

The back handspring step out (BHS) is a foundational skill in gymnastics balance beam routines that requires the generation of significant sagittal plane angular momentum while tightly regulating frontal plane momentum to control their balance. However, which body segments are critical for generating this momentum and successfully performing the BHS and whether skill level influences this generation remains unknown. Twenty-five gymnasts with a range of skill levels performed a BHS on a balance beam. The BHS was scored, and segmental contributions to whole-body angular momentum were analyzed during the take-off, flight, hand contact and landing phases. Angular momentum has previously been used to assess balance control, where higher ranges of frontal plane angular momentum are indicative of poorer balance control. There were no differences in segmental contributions to angular momentum during the take-off phase between high- and low-scoring groups. However, the low-scoring group had higher trunk contributions to frontal plane angular momentum after the take-off phase. The trailing leg was also found to be a large contributor to frontal plane angular momentum, and thus more likely than the leading leg to cause deviations in balance control. In the sagittal plane, momentum generation and skill level were weakly correlated, suggesting as gymnasts become more skilled, they produce larger sagittal plane motions and are more adept at generating angular momentum. Because the trunk and trailing leg had high contributions to frontal plane angular momentum, controlling the trunk and trailing leg should be a focus in training regimes to improve BHS performance.