Optimal Guidance Law with Impact-Angle Constraint and Acceleration Limit for Exo-Atmospheric Interception

This paper aims to develop an optimal guidance law for exo-atmospheric interception, in which impact-angle constraint and acceleration limit are considered. Firstly, an optimal control problem with constraints on terminal miss and impact-angle is formulated, in which the control energy performance index is weighted by a power function of the time-to-go. The closed-loop guidance command, which is expressed as a linear combination of zero-effort miss distance and the zero-effort angle error, is derived using a traditional order reduction transformation. Then, an analytical solution to the maximal acceleration during the flight is obtained by analyzing the boundary points and critical points of the guidance command curve. It is found that the maximal acceleration is a function of the weighted gain in the performance index. Therefore, the maximal acceleration can be efficiently limited by using the variable weighted gain. Furthermore, the relationship between the total control energy and the weighted gain is studied. As a result, a systematic method is proposed for selecting the weighted gain so as to meet the constraint of the acceleration while the total control energy is minimal. Nonlinear simulations have been carried out to test the performance of the proposed method. The results show that this method performs well in intercepting the maneuvering target with a negligible miss distance and intercept angle error. And it can tolerate a stricter acceleration limit in comparison with the typical method.

How far from the gold standard? Comparing the accuracy of a Local Position Measurement (LPM) system and a 15 Hz GPS to a laser for measuring acceleration and running speed during team sports

Purpose This study compared the validity and inter- and intra-unit reliability of local (LPM) and global (GPS) position measurement systems for measuring acceleration during team sports. Methods Devices were attached to a remote-controlled car and validated against a laser. Mean percentage biases (MPBs) of maximal acceleration (amax) and maximal running speed (vmax) were used to measure validity. Mean between-device and mean within-device standard deviations of the percentage biases (bd-SDs and wd-SDs) of amax and vmax were used to measure inter- and intra-unit reliability, respectively. Results Both systems tended to underestimate amax similarly (GPS: –61.8 to 3.5%; LPM: –53.9 to 9.6%). The MPBs of amax were lower in trials with unidirectional linear movements (GPS: –18.8 to 3.5%; LPM: −11.2 to 9.6%) than in trials with changes of direction (CODs; GPS: –61.8 to −21.1%; LPM: −53.9 to –35.3%). The MPBs of vmax (GPS: –3.3 to –1.0%; LPM: –12.4 to 1.5%) were lower than those of amax. The bd-SDs and the wd-SDs of amax were similar for both systems (bd-SDs: GPS: 2.8 to 12.0%; LPM 3.7 to 15.3%; wd-SDs: GPS: 3.7 to 28.4%; LPM: 5.3 to 27.2%), whereas GPS showed better bd-SDs of vmax than LPM. Conclusion The accuracy depended strongly on the type of action measured, with CODs displaying particularly poor validity, indicating a challenge for quantifying training loads in team sports.

Emergence of maximal acceleration from non-commutativity of spacetime

In this paper, we show that the causally connected four-dimensional line element of the [Formula: see text]-deformed Minkowski spacetime induces an upper cut-off on the proper acceleration and derive this maximal acceleration, valid up to first order in the deformation parameter. We find a contribution to maximal acceleration which is independent of [Formula: see text] and thus signals effect of the non-commutativity alone. We also construct the [Formula: see text]-deformed geodesic equation and obtain its [Formula: see text]-deformed Newtonian limit, valid up to first order in deformation parameter. Using this, we constrain non-commutative parameters present in the expression for maximal acceleration. We analyze different limits of the maximal acceleration and also discuss its implication to maximal temperature. We also obtain a bound on the deformation parameter.

Aceleraciones de alta intensidad en el fútbol. ¿Por qué es importante el método de evaluación? (High-intensity acceleration in soccer. Why is the evaluation method important?)

El objetivo del presente estudio fue analizar las posibles diferencias entre el uso de diferentes tipos de umbrales para evaluar los esfuerzos de alta intensidad, tanto en número como en distancia recorrida en jóvenes futbolistas de élite. Un total de 26 jóvenes jugadores fueron analizados durante 18 partidos oficiales (n = 108). Los esfuerzos de alta intensidad se evaluaron utilizando un umbral relativo individualizado basado en la capacidad de acelerar a diferentes velocidades iniciales, considerando la aceleración de alta intensidad cuando fue >75% de la capacidad máxima de acelerar (>75% amax). Se utilizó también un umbral >21 km·h-1 cuando la intensidad de la aceleración fue >75% amax, y umbrales absolutos >3 m·s-2 y >4 m·s-2, contabilizando tanto el número como la distancia (metros). El análisis post hoc mostró diferencias significativas por pares entre el uso de umbrales a alta intensidad (p < .05), en número y distancia. Los resultados mostraron que el uso de umbrales absolutos podría sobreestimar (>3 m·s-2) y subestimar (>4 m·s-2 y >21 km·h-1) esfuerzos de aceleración a alta intensidad (tanto en número como en distancia) en comparación con el uso de un umbral relativo individualizado (p < .05). Por lo tanto, concluimos que el uso de umbrales de aceleración absolutos (>3 m·s-2 y >4 m·s-2) puede no ser apropiado para analizar estos esfuerzos de alta intensidad en jóvenes futbolistas. Además, los umbrales de velocidad de carrera podrían subestimar las acciones de alta intensidad desarrolladas en una distancia corta, siendo más apropiados combinarlos con un umbral relativo individual para evaluar las acciones de alta intensidad en partidos de fútbol. Abstract. The aim of the current study was to analyze the possible differences between the use of different kinds of thresholds to assess high-intensity acceleration efforts, both in number and distance covered in young elite soccer players. A total of 26 young soccer players were analyzed during 18 competitive matches (n=108). High-intensity acceleration efforts were assessed using an individual relative threshold based on the capacity of acceleration from different initial speeds, considering high-intensity acceleration when it was >75% of the maximal acceleration (>75% amax). It was also used a threshold >21 km·h-1 when the acceleration intensity was >75% amax, and absolute thresholds of >3 m·s-2 and >4 m·s-2, both in number and distance (meters). Post hoc analysis showed pairwise significant differences between the use of high-intensity thresholds (p < .05), in number and distance. The results showed that the use of absolute thresholds could overestimate (>3 m·s-2) and underestimate (>4 m·s-2 and >21 km·h-1) high-intensity acceleration efforts (both in number and distance) in comparison with the use of an individual relative threshold (p < .05), whereas a threshold based on high-speed running could underestimate high-intensity acceleration efforts (p < .05). Therefore we conclude that the use of absolute acceleration thresholds (>3 m·s-2 and >4 m·s-2) may not be appropriate to analyze these efforts in young soccer players. In addition, speed running thresholds could underestimate high-intensity actions developed in short distance, being more appropriate to combine with an individual relative threshold to assess high-intensity action in soccer matches.

Gender Differences in Kinematic Parameters of Topspin Forehand and Backhand in Table Tennis

Background: The identification of gender differences in kinematics and coordination of movement in different body segments in sports may improve the training process by emphasizing the necessity of its differentiation, and consequently individualization, developing, and improving the technique in women and men. Indicating differences can also help in determining the risk of injury in order to prevent from them by diversifying training programs. However, there is no information regarding this problem in the existing literature pertaining to table tennis. Therefore, the aim of the study was to evaluate the differences in the values of selected angular and kinematic parameters during topspin forehand and topspin backhand shots between male and female table tennis players. Methods: Six male and six female advanced table tennis players performed topspin forehand and topspin backhand shots, both receiving a backspin ball. The angular parameters in four events (ready position, backswing, maximum acceleration, and forward) at chosen joints as well as the maximal acceleration of the playing hand were measured, using the myoMotion system, and were compared between male and female players. Results: Significant differences (p ≤ 0.05) were found in the magnitude of angular parameters and maximum hand acceleration between men and women. The movement pattern of topspin strokes performed by men takes into account, more than that in the case of women, movements that use large muscle groups and large joints (hip joints, trunk joints, shoulder joints in extension, and flexion). The difference in the values of maximal acceleration reached almost 50 m/s2 in topspin forehand (p < 0.01) and 20 m/s2 in backhand (p < 0.01). Conclusions: Differentiation of movement patterns can be a manifestation of movement optimization due to anthropological differences and limitations. The differences in the values of maximal acceleration suggest that women could use both sides to perform a topspin attack against the backspin ball, while men should seek opportunities to make a stronger shot with a forehand topspin.

Endurance of the Dorsal and Ventral Muscles in the Neck

Endurance of the muscles of the neck are rarely studied. This study measured the endurance index (EI) of the sternocleidomastoid (SCM) and upper trapezius muscles of the neck (trap). The vastus lateralis (VL) was used for comparison. Skeletal muscle endurance of twelve healthy subjects, age 19–22 years, were tested on their SCM and trap in random order on one day, VL was tested on a separate day. Participants were tested in the supine position for the SCM and VL muscles and the prone position for the trap. Muscle contractions consisted of a 5 Hz twitch electrical stimulation for 5 min. Muscle acceleration (resultant vector) was measured using a triaxial accelerometer. EI was the ending acceleration as a percentage of the maximal acceleration. The endurance index (EI) for the SCM, trap, and VL was 42.3 ± 13.0%, 42.3 ± 20.2%, and 92.9 ± 11.0%, respectively. The EI of the VL was significantly higher than the EI of the SCM (t(2,22) = 10.33, p < 0.001) and the trap (t(2,22) = 7.625, p < 0.001). The EI was not different between the SCM and the trap muscle (t(2,22) = 0.004, p = 0.997). In conclusion, the neck muscles had much less endurance than the muscles in the leg and could make fatigued athletes more susceptible to concussions caused by head impacts.

Application of Polynomial Transition Curves for Trajectory Planning on the Headlands

This paper presents a method of polynomial transition curve application for making agricultural aggregate movement paths during headland turn drives as well as within the field. Four types of agricultural aggregate paths in five different variant designs are discussed. Each path is composed of only two curves, making the so-called transition bi-curve. The curvature described by the linear function as well as the third, fifth, seventh, and ninth degree polynomials was designated. Moreover, a trajectory planning algorithm in which the movement proceeds along two transition curves composing the so-called bi-curve was proposed. The simulation was carried out applying the MATLAB program in which the 4th order Runge–Kutta method was used. The results were presented by means of figures showing the proposed paths and kinematic quantity courses in the displacement function. The obtained trajectories were compared regarding the size and kinematic quantities. The trajectories, whose curvature is described by the 3° polynomial, were found to possess the smallest absolute values of maximal acceleration and jerk and to lack jerk discontinuity. The proposed solutions can be applied for planning trajectory of not only agriculture machines and aggregates but also autonomous vehicles or mobile robots.