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Content available remote Random jumps with free partially deterministic coalescence
EN
The aim of this paper is to discuss a special case of a coalescing random jumps model of infinitely many jumping individuals. Jumps are embedded with repulsion at the target point and coalescence kernel is defined in such a way that for two coalescing individuals the result is deterministically defined. A possible approach to study the dynamics of the system numerically is discussed. It is based on a Poisson approximation of states of the system. Some interesting results of simulations are showed.
PL
Celem niniejszego artykułu jest omówienie szczególnego przypadku modelu skoków z odpychaniem oraz ze sklejaniem opisującego dynamikę nieskończonej liczby agentów. Skoki są wyposażone w mechanizm odpychania oparty o punkt docelowy skoku. Jądro koalescencji jest zdefiniowane w taki sposób, że wynik sklejania dwóch agentów jest określony w sposób deterministyczny. Podany został przykład podejścia do badania numerycznego dynamiki tego modelu opierający się o przybliżanie stanów układu miarami Poissona. Pokazano kilka ciekawych rezultatów takich symulacji.
EN
Vertical jump height is recognised as a determinant factor in elite volleyball performance. In previous studies there are different opinions on whether vertical jump height performance improves during maturation or not. The aim of this study was to assess the differences in jumping abilities in two different age groups of female volleyball players and to determine the take-off efficiency during repeated jumps. Methods: Seventeen female volleyball players from two different age categories – adults and under 16 years – participated in this study. Quattro Jump 9290BA force platform (Kistler, Winterthur, Switzerland) was used to assess the jumping performance during squat jumps, counter movement jumps, and 45-second continuous jumps. Results: Jumping performance did not differ significantly between the two groups. The main efficiency of the conversion of mechanical work into mechanical energy was only 24% and it decreased during the test. Conclusions: The influence of age on the jumping performance in a group of female volleyball players was not confirmed. Take-off efficiency was in both groups quite low and it did not improve during the test.
EN
This study aimed to explore the effect of fatigue on the biomechanical contribution of the lower extremity joints during a typical stretch-shortening cycle (SSC) task. Methods: 15 male athletes completed drop jump (DJ) under pre- and post-fatigue. Vicon motion capture system and 3D Kistler force plates were used to collect kinematics and ground reaction force data simultaneously. Results: Under fatigue condition, 1) the DJ height decreased; the touchdown angle of knee and ankle reduced and the range of motion increased; 2) the maximum push-off moment and power of knee was reduced; 3) the stiffness of knee, ankle, and legs was reduced; 4) the energy generation and the net energy of the ankle decreased; 5) the energy contribution of knee decreased during the eccentric phase. Conclusions: Fatigue altered biomechanical contribution of the lower extremity joints by changing the movement pattern during DJ. The control ability of the knee and ankle were decreased. Eventually, the jump performance was reduced. In addition, the decrease of stiffness as well as the energy contribution of these joints can be used as sensitive indices to evaluate the performance of DJ after fatigue.
EN
Purpose: One inconvenience in finding experimental evidence for the relationship between potential elastic energy and vertical jump height is the difficulty of estimating the value of the stored potential elastic energy. Therefore, the aim of this study is to present a simple method of estimating the potential elastic energy stored by lowering the center of mass during the countermovement phase of a vertical jump. Methods: The research was conducted on 30 able-bodied male university students (age: 20 years, body height: 183.1 ± 7.9 cm, body mass: 80.3 ± 10.4 kg). Each participant performed 10 single countermovement jumps with arms akimbo to maximal height. Measurements employed a Kistler force plate. The value of potential elastic energy was estimated based on the curve of dependence of the ground reaction force on the vertical displacement of the jumper’s center of mass. Results: The mean value (±SD) of potential elastic energy collected due to lowering of the center of mass during the countermovement phase of a vertical jump was 183 ± 69 J. 24.3% of this value can be considered the part of the potential elastic energy (44 ± 21 J) that comes from the transformation of kinetic energy. The total change in gravitational potential energy due to lowering the center of mass was 240 ± 58 J. Conclusions: This estimation of potential elastic energy is only general and rough. However, certain estimations of potential elastic energy may offer some insight into the phenomenon relating vertical quasi-stiffness and the ability to store potential elastic energy with vertical jump height.
EN
Vertical jump tests are used to assess lower-limb power of athletes in sport sciences. Flight time measurement with jump-mat systems is the most common procedure for this purpose. The aim of this study was to analyze the concurrent validity and reliability of two proprietary systems (Globus and Axon) and an open-source system (Chronojump). Methods: A conditioning electric circuit governed by a controlled wave generator is designed to substitute athletes jumping on a physical mat. In order to look for possible differences associated to timekeeping by each microcontroller device, all three systems are fed by the circuit simultaneously. Results: Concurrent validity was high for the three systems. Standarized typical error of estimate (TEE) was trivial, according to MBI interpretation, as well as perfect Pearson correlation coefficient. Reliability was assessed using coefficient of variation of flight time measure, resulting in 0.17–0.63% (0.05–0.12 cm) for Globus, 0.01% (0.09 cm) for Chronojump and 5.65–9.38% (2.15–3.53 cm) for Axon. These results show that all jump-mat system produced nearly identical measures of flight time so they can be considered valid and reliable for practical purposes. In comparison, Chronojump showed the best performance whereas Axon showed enough variability and disagreement to pose a problem in testing elite athletes. Conclusions: These experiments show that open-source jump mats are as valid and reliable as their proprietary counterparts at a lower cost. Therefore, practitioners can be confident in using Globus or Chronojump systems to test athletes’ jump height because of their negligible errors and Axon system to monitor general population.
EN
The objective of this study was to evaluate the reliability and validity of two alternative systems used for jumping performance measurement. Methods: Two groups of subjects were tested. The first group consisted of 15 male adults (21.3 ± 1.7 years ) and the second group consisted of 16 female volleyball players (17.2 ± 0.9 years). We used three different systems of data collection in the study. Two of the used systems are based on optoelectric components. The Optojump Next system is referred to as the optoelectric system, and BTS Smart-E is refered to as the video system. Concurrent validity of these systems was verified with the use of “gold standard” which is force platform. All systems were used to estimate the height of vertical jumps. Results: Both optoelectric systems occurred to be highly reliable with the ICCs=0.98 for Optojump and 0.9 for BTS Smart. Their concurrent validity with the force platform data was also very high r=0.99 and r=0.97 respectively. Conclusions: Comparison of these two systems shows distinct differences between them where Optojump system is more suitable for quick and reliable sports testing, when BTS-Smart for research and clinical testing.
EN
Purpose: Lower extremity power is an important physical capacity of a soccer athlete. Power represents, and can be modified by, the training of strength and speed. Pre-season and in-season training differs in the relative emphasis on these two quantities. It is nevertheless desirable that the mechanical power remain the same or become higher during the in-season period. The purpose of this study was to identify changes in quantities related to “explosive strength” and to check whether, in collegiate female soccer players, pre- and inseason lower extremity power will remain unaltered. Methods: Twenty collegiate female soccer players, representing all field positions, participated. Lower extremity power was assessed by a series of drop jumps executed from four different heights (15, 30, 45, and 60 cm). Mechanical power was calculated using subject’s mass, jump height, and acceleration due to gravity. This value was further normalized by body mass of each athlete to obtain the relative (or normalized) mechanical power. Results: The normalized lower extremity mechanical power was highest when landing from the 30 cm height for both pre- and inseason periods. However, contrary to expectations, it turned out lower during the in-season than during the pre-season test, even though no significant differences were found between the corresponding jump heights. Conclusions: It is concluded that altered, perhaps inadequate, training strategies were employed during the in-season period. Besides, advantages of adding the relative mechanical power as a season readiness indicator are underlined compared with relying on the jump height alone.
EN
Understanding leg and joint stiffness adjustment during maximum hopping may provide important information for developing more effective training methods. It has been reported that ankle stiffness has major influence on stable spring-mass dynamics during submaximal hopping, and that knee stiffness is a major determinant for hopping performance during maximal hopping task. Furthermore, there are no reports on how the height of the previous hop could affect overall stiffness modulation of the subsequent maximum one. The purpose of the present study was to determine whether and how the jump height of the previous hop affects leg and joint stiffness for subsequent maximum hop. Ten participants completed trials in which they repeatedly hopped as high as possible (MX task) and trials in which they were instructed to perform several maximum hops with 3 preferred (optimal) height hops between each of them (P3MX task). Both hopping tasks were performed at 2.2 Hz hopping frequency and at the participant's preferred (freely chosen) frequency as well. By comparing results of those hopping tasks, we found that ankle stiffness at 2.2 Hz (p=0.041) and knee stiffness at preferred frequency (p=0.045) was significantly greater for MX versus P3MX tasks. Leg stiffness for 2.2 Hz hopping is greater than for the preferred frequency. Ankle stiffness is greater for 2.2 Hz than for preferred frequencies; opposite stands for knee stiffness. The results of this study suggest that preparatory hop height can be considered as an important factor for modulation of maximum hop.
EN
The aim of this research was to evaluate the biomechanical parameters of lower limbs and their influence on height of vertical jump. The research was conducted on a group of females practicing basketball and volleyball. The following equipment was used during the experiment: a force plate by Kistler, a Biometrics electrogoniometer and a specially designed chair to measure static torque by OPIW Opole. The results indicated that the jumping abilities of the examined athletes were poor. No statistically significant correlations were observed between knee static torque and heights of vertical jumps: CMJ and DJ. The authors suggest modification of the McClymont index (RSI) to evaluate the selection of platform height during plyometric training. Such modification would enable better choice of loads and better training control of the subject.
PL
Artykuł przedstawia model do badania dynamiki salta w tył na batucie. Skaczącego zamodelowano za pomocą układu sześciu połączonych ze sobą przegubowo ciał sztywnych, realizującego ruch płaski o ośmiu stopniach swobody. Zastosowany formalizm matematyczno-fizyczny umożliwia, w kategoriach zagadnienia odwrotnego dynamiki, obliczanie wymaganych momentów sterujących (momentów sił mięśniowych) podczas analizowanego skoku oraz wyznaczanie nieznanych reakcji więzów podczas kontaktu skaczącego z batutem.
EN
The paper presents a model for studying dynamics of a backward somersault on the trampoline. The planar, six-link, joint-connected system of rigid bodies with eight degrees of freedom is presented. The applied mathematical-physical formalism allows one, in terms of inverse dynamics problem, to determine the required control inputs (articular torques) during a specified spring and the unknown constraint reaction forces during the contact with the trampoline.
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