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14 pages, 1322 KiB  
Article
Applying a Virtual Art Therapy System Based on the Michelangelo Effect in Patients with Spinal Cord Injury
by Michela Franzò, Sara De Angelis, Marco Iosa, Gaetano Tieri, Giorgia Corsini, Giovanni Generoso Cellupica, Valentina Loi, Fabiano Bini, Franco Marinozzi, Giorgio Scivoletto and Federica Tamburella
Sensors 2025, 25(13), 4173; https://doi.org/10.3390/s25134173 - 4 Jul 2025
Viewed by 336
Abstract
Background: Serious videogames have already demonstrated their positive impact on rehabilitation and of particular interest is the virtual reality (VR) technology. This immersive technology has been used in this study to create a neuroaesthetic experience based on the Michelangelo effect for the rehabilitation [...] Read more.
Background: Serious videogames have already demonstrated their positive impact on rehabilitation and of particular interest is the virtual reality (VR) technology. This immersive technology has been used in this study to create a neuroaesthetic experience based on the Michelangelo effect for the rehabilitation of patients with spinal cord injury. The aim of this study was to test the usability of a system for virtual art therapy and its capacity to assess patients’ deficits performances. Methods: A VR headset was worn by the participants who experienced a painting simulation of famous artworks (artistic stimuli) against a coloring canvas (non-artistic stimuli). The trajectories of the hand were studied to obtain different kinematic and spectral parameters to evaluate the user performances. A total of 13 healthy subjects and 13 patients with spinal cord injury participated in this study. Results: Significative differences were obtained for most of the parameters between the two groups, except for the normalized jerk and energy of the spectrum. Analysis in the frequency domain showed that both groups preferred horizontal movements for painting the canvas. The NASA and USEQ scores reported a comfortable and user-friendly system according to the patients’ point of view. Conclusions: The system can be a usable tool, the rehabilitative efficacy of which should be tested in patients with spinal cord injury. The kinematic and spectral parameters would allow for the evaluation of the performances alongside the clinical scales, distinguish pathological and physiological performances. Full article
(This article belongs to the Special Issue Sensors in 2025)
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20 pages, 13323 KiB  
Article
Dynamic Weight Model Predictive Control for Longitudinal Adaptive Cruise Systems in Electric Vehicles
by Wentian Wei, Lan Li, Qiyuan Li, Song Zhang, Chaoqun Fan and Lizhe Liang
Appl. Sci. 2025, 15(12), 6715; https://doi.org/10.3390/app15126715 - 16 Jun 2025
Cited by 1 | Viewed by 579
Abstract
This paper proposes a dynamic weight model predictive control (DWMPC) strategy for adaptive cruise control (ACC) in pure electric vehicles, aiming to enhance robustness, energy efficiency, and ride comfort under complex traffic conditions. Unlike conventional MPC with static weights, the proposed method integrates [...] Read more.
This paper proposes a dynamic weight model predictive control (DWMPC) strategy for adaptive cruise control (ACC) in pure electric vehicles, aiming to enhance robustness, energy efficiency, and ride comfort under complex traffic conditions. Unlike conventional MPC with static weights, the proposed method integrates a fuzzy inference system that evaluates driving urgency based on real-time spacing and velocity errors. The resulting emergency coefficient is mapped through a nonlinear function to dynamically adjust the velocity tracking weight in the MPC cost function. Additionally, a four-mode coordination mechanism adaptively modifies acceleration and jerk penalties according to risk levels, enabling balanced responses between safety and comfort. A composite performance evaluation index (PEI) is formulated to quantitatively assess energy consumption, ride comfort, spacing accuracy, and emergency responsiveness. Simulation results under WLTC and typical urban driving scenarios demonstrate that DWMPC outperforms fixed-weight MPC and PI controllers, reducing energy consumption by 6.5%, jerk by 42.9%, and response time by 41.8% while improving coordination in speed tracking, inter-vehicle distance regulation, and energy-efficient control. Full article
(This article belongs to the Section Transportation and Future Mobility)
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18 pages, 4888 KiB  
Article
A Multimodal Fatigue Detection System Using sEMG and IMU Signals with a Hybrid CNN-LSTM-Attention Model
by Soree Hwang, Nayeon Kwon, Dongwon Lee, Jongman Kim, Sumin Yang, Inchan Youn, Hyuk-June Moon, Joon-Kyung Sung and Sungmin Han
Sensors 2025, 25(11), 3309; https://doi.org/10.3390/s25113309 - 24 May 2025
Viewed by 1109
Abstract
Physical fatigue significantly impacts safety and performance across industrial, athletic, and medical domains, yet its detection remains challenging due to individual variability and limited generalizability of existing methods. This study introduces a multimodal fatigue detection system integrating surface electromyography (sEMG) and inertial measurement [...] Read more.
Physical fatigue significantly impacts safety and performance across industrial, athletic, and medical domains, yet its detection remains challenging due to individual variability and limited generalizability of existing methods. This study introduces a multimodal fatigue detection system integrating surface electromyography (sEMG) and inertial measurement unit (IMU) signals, processed through a hybrid convolutional neural network–long short-term memory–attention (CNN-LSTM-Attention) model. Fatigue was induced in 35 healthy participants via step-up-and-down exercises, with gait data collected during natural walking before and after fatigue. The model leverages sEMG from the gastrocnemius lateralis and IMU-derived jerk signals from the tibialis anterior and rectus femoris to classify fatigue states. Evaluated using leave-one-subject-out cross-validation (LOSOCV), the system achieved an accuracy of 87.94% with bilateral EMG signals and a balanced recall of 87.94% for fatigued states using a combined IMU-EMG approach. These results highlight the system’s robustness for personalized fatigue monitoring, surpassing traditional subject-dependent methods by addressing inter-individual differences. Full article
(This article belongs to the Special Issue Wearable Sensing of Medical Condition at Home Environment)
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20 pages, 1942 KiB  
Article
Operator Expertise in Bilateral Teleoperation: Performance, Manipulation, and Gaze Metrics
by Harun Tugal, Ihsan Tugal, Fumiaki Abe, Masaki Sakamoto, Shu Shirai, Ipek Caliskanelli and Robert Skilton
Electronics 2025, 14(10), 1923; https://doi.org/10.3390/electronics14101923 - 9 May 2025
Cited by 2 | Viewed by 796
Abstract
This paper presents a comprehensive user study aimed as assessing and differentiating operator expertise within bilateral teleoperation systems. The primary objective is to identify key performance metrics that effectively distinguish novice from expert users. Unlike prior approaches that focus primarily on psychological evaluations, [...] Read more.
This paper presents a comprehensive user study aimed as assessing and differentiating operator expertise within bilateral teleoperation systems. The primary objective is to identify key performance metrics that effectively distinguish novice from expert users. Unlike prior approaches that focus primarily on psychological evaluations, this study emphasizes direct performance analysis across a range of telerobotic tasks. Ten participants (six novices and four experts) were assessed based on task completion time and difficulty, error rates, manipulator motion characteristics, gaze behaviour, and subjective feedback via questionnaires. The results show that experienced operators outperformed novices by completing tasks faster, making fewer errors, and demonstrating smoother manipulator control, as reflected by reduced jerks and higher spatial precision. Also, experts maintained consistent performance even as task complexity increased, whereas novices experienced a sharp decline, particularly at higher difficulty levels. Questionnaire responses further revealed that novices experienced higher mental and physical demands, especially in unfamiliar tasks, while experts demonstrated higher concentration and arousal levels. Additionally, the study introduces gaze transition entropy (GTE) and stationary gaze entropy (SGE) metrics to quantify visual attention strategies, with experts exhibiting more focused, goal-oriented gaze patterns, while novices showed more erratic and inefficient behaviour. These findings highlight both quantitative and qualitative measures as critical for evaluating operator performance and informing future teleoperation training programs. Full article
(This article belongs to the Special Issue Haptic Systems and the Tactile Internet: Design and Applications)
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16 pages, 13982 KiB  
Article
Exploring Chaos in Fractional Order Systems: A Study of Constant and Variable-Order Dynamics
by Reem Allogmany, Nada A. Almuallem, Reima Daher Alsemiry and Mohamed A. Abdoon
Symmetry 2025, 17(4), 605; https://doi.org/10.3390/sym17040605 - 16 Apr 2025
Viewed by 512
Abstract
Fractional calculus generalizes well-known differentiation and integration to noninteger orders, allowing a more accurate framework for modeling complex dynamical behaviors. The application of fractional-order systems is quite wide in engineering, biology, and physics because they inherently capture the memory effects and long-range dependencies. [...] Read more.
Fractional calculus generalizes well-known differentiation and integration to noninteger orders, allowing a more accurate framework for modeling complex dynamical behaviors. The application of fractional-order systems is quite wide in engineering, biology, and physics because they inherently capture the memory effects and long-range dependencies. Out of these, fractional jerk chaotic systems have gained attention regarding their applications in secure communication, signal processing, and control systems. This work develops a comparative analysis of a fractional jerk system that includes constant- and variable-order derivatives to contribute to chaos–stability analysis. Additionally, this study uncovers novel chaotic behaviors, further expanding our understanding of complex dynamical systems. The results yield new insights into using variable-order dynamics to enable chaotic systems to better adapt to real applications. Full article
(This article belongs to the Special Issue Symmetry and Its Applications in Partial Differential Equations)
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16 pages, 3688 KiB  
Article
Adapting Young Adults’ In-Shoe Motion Sensor Gait Models for Knee Evaluation in Older Adults: A Study on Osteoarthritis and Healthy Knees
by Chenhui Huang, Kenichiro Fukushi, Haruki Yaguchi, Keita Honda, Yusuke Sekiguchi, Zhenwei Wang, Yoshitaka Nozaki, Kentaro Nakahara, Satoru Ebihara and Shin-Ichi Izumi
Sensors 2025, 25(7), 2167; https://doi.org/10.3390/s25072167 - 28 Mar 2025
Viewed by 613
Abstract
The human knee joint is crucial for mobility, especially in older adults who are susceptible to conditions like osteoarthritis (OA). Traditionally, assessing knee health requires complex gait analysis in clinical settings, which limits opportunities for convenient and continuous monitoring. This study leverages advancements [...] Read more.
The human knee joint is crucial for mobility, especially in older adults who are susceptible to conditions like osteoarthritis (OA). Traditionally, assessing knee health requires complex gait analysis in clinical settings, which limits opportunities for convenient and continuous monitoring. This study leverages advancements in wearable technology to explore the adaptation of models based on in-shoe motion sensors (IMS), initially trained on young adults, for evaluating knee function in older populations, both healthy and with OA. Data were collected from 44 older OA patients, presenting various levels of severity, and 20 healthy older adults, with a focus on key knee indicators: knee angle measures (S1 to S3), temporal gait parameters (S4 and S5), and knee angular jerk cost metrics (S6 to S8). The models effectively identified trends and differences across these indicators between the healthy group and the OA group. Notably, in indicators S1, S2, S3, S7, and S8, the models exhibited a large effect size in correlation with true values. These findings suggest that gait models derived from younger, healthy individuals are possible to be robustly adapted for non-invasive, everyday monitoring of knee health in older adults, offering valuable insights for the early detection and management of knee impairments. However, limitations such as fixed biases due to differences in measurement systems and sensor placement inaccuracies were identified. Future research will aim to enhance model precision by addressing these limitations through domain adaptation techniques and improved sensor calibration. Full article
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17 pages, 9669 KiB  
Article
A Passive Experiment on Route Bus Speed Change Patterns to Clarify Electrification Benefits
by Yiyuan Fang, Wei-Hsiang Yang and Yushi Kamiya
World Electr. Veh. J. 2025, 16(3), 178; https://doi.org/10.3390/wevj16030178 - 17 Mar 2025
Viewed by 644
Abstract
In addition to the widely recognized benefits of reducing carbon emissions and protecting the environment, the authors believe that bus electrification has potential advantages in enhancing driving safety, improving passenger comfort, and reducing driver fatigue—areas that have not yet been sufficiently studied and [...] Read more.
In addition to the widely recognized benefits of reducing carbon emissions and protecting the environment, the authors believe that bus electrification has potential advantages in enhancing driving safety, improving passenger comfort, and reducing driver fatigue—areas that have not yet been sufficiently studied and emphasized. Safety and comfort are fundamental objectives in the continuous development of transportation systems. They are directly and closely related to both passengers and drivers and are among the top priorities when individuals choose their mode of transportation. Therefore, these aspects deserve broader and more in-depth attention and research. This study aims to identify the potential advantages of route bus electrification in terms of safety and comfort. The results of a passive experiment on the speed profile of buses operating on actual routes are presented here. Firstly, we focus on the acceleration/deceleration at the starting/stopping stops, specifically for regular-route buses, and obtain the following information: I. Starting acceleration from a bus stop is particularly strong in the second half of the acceleration process, being suitable for motor-driven vehicles. II. The features of the stopping deceleration at a bus stop are “high intensity” and “low dispersion”, with the latter enabling the refinement of regenerative settings and significantly lowering electricity economy during electrification. And we compare the speed profile of an electric bus with those of a diesel bus and obtain the following information: III. Motor-driven vehicles offer the advantages of “high acceleration performance” and “no gear shifting”, making them particularly suitable for the high-intensity acceleration required when route buses depart from stations. This not only simplifies driving operations but also enhances lane-changing safety. And by calculating and analyzing the jerk amount, we could quantitatively demonstrate the comfortable driving experience while riding on this type of bus where there is no shock due to gear shifting. IV. While the “high acceleration performance” of motor-driven vehicles produces “individual differences in the speed change patterns”, this does not translate to “individual differences in electricity consumption”, owing to the characteristics of this type of vehicle. With engine-driven vehicles, measures such as “slow acceleration” and “shift up early” are strongly encouraged to realize eco-driving, and any driving style that deviates from these measures is avoided. However, with motor-driven vehicles, the driver does not need to be too concerned about the speed change patterns during acceleration. This characteristic also suggests a benefit in terms of the electrification of buses. Full article
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30 pages, 24605 KiB  
Article
Advanced Trajectory Analysis of NASA’s Juno Mission Using Unsupervised Machine Learning: Insights into Jupiter’s Orbital Dynamics
by Ashraf ALDabbas, Zaid Mustafa and Zoltan Gal
Future Internet 2025, 17(3), 125; https://doi.org/10.3390/fi17030125 - 11 Mar 2025
Viewed by 1186
Abstract
NASA’s Juno mission, involving a pioneering spacecraft the size of a basketball court, has been instrumental in observing Jupiter’s atmosphere and surface from orbit since it reached the intended orbit. Over its first decade of operation, Juno has provided unprecedented insights into the [...] Read more.
NASA’s Juno mission, involving a pioneering spacecraft the size of a basketball court, has been instrumental in observing Jupiter’s atmosphere and surface from orbit since it reached the intended orbit. Over its first decade of operation, Juno has provided unprecedented insights into the solar system’s origins through advanced remote sensing and technological innovations. This study focuses on change detection in terms of Juno’s trajectory, leveraging cutting-edge data computing techniques to analyze its orbital dynamics. Utilizing 3D position and velocity time series data from NASA, spanning 11 years and 5 months (August 2011 to January 2023), with 5.5 million samples at 1 min accuracy, we examine the spacecraft’s trajectory modifications. The instantaneous average acceleration, jerk, and snap are computed as approximations of the first, second, and third derivatives of velocity, respectively. The Hilbert transform is employed to visualize the spectral properties of Juno’s non-stationary 3D movement, enabling the detection of extreme events caused by varying forces. Two unsupervised machine learning algorithms, DBSCAN and OPTICS, are applied to cluster the sampling events in two 3D state spaces: (velocity, acceleration, jerk) and (acceleration, jerk, snap). Our results demonstrate that the OPTICS algorithm outperformed DBSCAN in terms of the outlier detection accuracy across all three operational phases (OP1, OP2, and OP3), achieving accuracies of 99.3%, 99.1%, and 98.9%, respectively. In contrast, DBSCAN yielded accuracies of 98.8%, 98.2%, and 97.4%. These findings highlight OPTICS as a more effective method for identifying outliers in elliptical orbit data, albeit with higher computational resource requirements and longer processing times. This study underscores the significance of advanced machine learning techniques in enhancing our understanding of complex orbital dynamics and their implications for planetary exploration. Full article
(This article belongs to the Special Issue AI and Security in 5G Cooperative Cognitive Radio Networks)
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26 pages, 7333 KiB  
Article
Takagi–Sugeno–Kang Fuzzy Neural Network for Nonlinear Chaotic Systems and Its Utilization in Secure Medical Image Encryption
by Duc Hung Pham and Mai The Vu
Mathematics 2025, 13(6), 923; https://doi.org/10.3390/math13060923 - 11 Mar 2025
Cited by 3 | Viewed by 886
Abstract
This study introduces a novel control framework based on the Takagi–Sugeno–Kang wavelet fuzzy neural network, integrating brain imitated network and cerebellar network. The proposed controller demonstrates high robustness, making it an excellent candidate for handling intricate nonlinear dynamics, effectively mapping input–output relationships and [...] Read more.
This study introduces a novel control framework based on the Takagi–Sugeno–Kang wavelet fuzzy neural network, integrating brain imitated network and cerebellar network. The proposed controller demonstrates high robustness, making it an excellent candidate for handling intricate nonlinear dynamics, effectively mapping input–output relationships and efficiently learning from data. To enhance its performance, the controller’s parameters are fine-tuned using Lyapunov stability theory. Compared to existing approaches, the proposed model exhibits superior learning capabilities and achieves outstanding performance metrics. Furthermore, the study applies this synchronization technique to the secure transmission of medical images. By encrypting a medical image into a chaotic trajectory before transmission, the system ensures data security. On the receiving end, the original image is successfully reconstructed using chaotic trajectory synchronization. Experimental results confirm the effectiveness and reliability of the proposed neural network model, as well as the encryption and decryption process. Specifically, the average_RMSE of the Takagi–Sugeno–Kang fuzzy wavelet brain cerebral controller (TFWBCC) method is 2.004 times smaller than the cerebellar model articulation controller (CMAC) method, 1.923 times smaller than the RCMAC method, 1.8829 times smaller than the TSKCMAC method, and 1.8153 times smaller than the brain emotional learning controller (BELC) method. Full article
(This article belongs to the Special Issue Advancements in Nonlinear Control Strategies)
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17 pages, 2842 KiB  
Article
A Comparative Study of Brownian Dynamics Based on the Jerk Equation Against a Stochastic Process Under an External Force Field
by Adriana Ruiz-Silva, Bahia Betzavet Cassal-Quiroga, Rodolfo de Jesus Escalante-Gonzalez, José A. Del-Puerto-Flores, Hector Eduardo Gilardi-Velazquez and Eric Campos
Mathematics 2025, 13(5), 804; https://doi.org/10.3390/math13050804 - 28 Feb 2025
Viewed by 638
Abstract
Brownian motion has been studied since 1827, leading to numerous important advances in many branches of science and to it being studied primarily as a stochastic dynamical system. In this paper, we present a deterministic model for the Brownian motion for a particle [...] Read more.
Brownian motion has been studied since 1827, leading to numerous important advances in many branches of science and to it being studied primarily as a stochastic dynamical system. In this paper, we present a deterministic model for the Brownian motion for a particle in a constant force field based on the Ornstein–Uhlenbeck model. By adding one degree of freedom, the system evolves into three differential equations. This change in the model is based on the Jerk equation with commutation surfaces and is analyzed in three cases: overdamped, critically damped, and underdamped. The dynamics of the proposed model are compared with classical results using a random process with normal distribution, where despite the absence of a stochastic component, the model preserves key Brownian motion characteristics, which are lost in stochastic models, giving a new perspective to the study of particle dynamics under different force fields. This is validated by a linear average square displacement and a Gaussian distribution of particle displacement in all cases. Furthermore, the correlation properties are examined using detrended fluctuation analysis (DFA) for compared cases, which confirms that the model effectively replicates the essential behaviors of Brownian motion that the classic models lose. Full article
(This article belongs to the Special Issue Mathematical Modelling of Nonlinear Dynamical Systems)
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11 pages, 1016 KiB  
Article
Smooth Moves: Comparing Log Dimensionless Jerk Metrics from Body Center of Mass Trajectory and Wearable Sensor Acceleration During Walking
by Paolo Brasiliano, Gaspare Pavei and Elena Bergamini
Sensors 2025, 25(4), 1233; https://doi.org/10.3390/s25041233 - 18 Feb 2025
Cited by 1 | Viewed by 996
Abstract
Movement smoothness is a critical metric for evaluating motor control and sensorimotor impairments, with increasing relevance in neurorehabilitation and everyday functional assessments. This study investigates the correlation between two smoothness metrics (Log Dimensionless Jerk): LDLJV, derived from body center of mass (BCoM) trajectories [...] Read more.
Movement smoothness is a critical metric for evaluating motor control and sensorimotor impairments, with increasing relevance in neurorehabilitation and everyday functional assessments. This study investigates the correlation between two smoothness metrics (Log Dimensionless Jerk): LDLJV, derived from body center of mass (BCoM) trajectories using a gold-standard stereophotogrammetric system, and LDLJA, calculated from acceleration data recorded via an inertial measurement unit (IMU) placed at the L1–L2 level. Ten healthy adults (six men and four women; height: 1.71 ± 0.08 m; body mass: 68.2 ± 10.2 kg; age: 34.5 ± 8.5 years) walked on a treadmill at seven different speeds, with stride-specific data analyzed to compute smoothness indices for three anatomical components (antero-posterior, medio-lateral, cranio-caudal). Concordance between the metrics was evaluated using Bland–Altman analysis, Spearman’s correlation, and the mean absolute percentage error. The results revealed weak correlations and substantial biases across all components and speeds, reflecting inherent differences between IMU- and BCoM-derived data. Correcting biases improved alignment but did not eliminate discrepancies. The findings highlight that LDLJA captures only localized trunk accelerations, whereas BCoM-derived LDLJV approximates whole-body dynamics, making direct substitution infeasible. This study emphasizes the need for careful interpretation of IMU-based metrics and contributes to refining their application in real-world gait analyses. Full article
(This article belongs to the Collection Sensors for Gait, Human Movement Analysis, and Health Monitoring)
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16 pages, 19985 KiB  
Article
A Chaotic Jerk Oscillator with Complete Control via Fractional Exponentiation and Its Experimental Analog Circuit Realization
by Menghui Shen, Chunbiao Li, Xiaoliang Cen, Manyu Zhao, Yuanxiao Xu and Ludovico Minati
Symmetry 2025, 17(2), 174; https://doi.org/10.3390/sym17020174 - 24 Jan 2025
Cited by 1 | Viewed by 790
Abstract
By introducing fractional exponentiation into a three-dimensional chaotic system, a jerk system with only six terms is designed. It has the property of total amplitude control, where a single non-bifurcation parameter can directly rescale all system variables without affecting the dynamics. It also [...] Read more.
By introducing fractional exponentiation into a three-dimensional chaotic system, a jerk system with only six terms is designed. It has the property of total amplitude control, where a single non-bifurcation parameter can directly rescale all system variables without affecting the dynamics. It also features two-dimensional offset boosting, where a single parameter can realize direct offset boosting while another provides interlocked cross-dimensional offset boosting. Furthermore, this jerk system has a parameter-dominated symmetric attractor, which means that symmetric attractors appear successively as the parameter changes from positive to negative. Circuit experiments confirm the feasibility of analog fractional exponentiation using the 444 circuit and the complete control, including amplitude control and offset boosting, of the resulting system. The proposed circuit may facilitate applications of chaotic signal generators where signal versatility is important and exemplifies the generative potential of analog fractional exponentiation. Full article
(This article belongs to the Section Engineering and Materials)
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11 pages, 1320 KiB  
Article
Effect of Post-Activation Potentiation on Weightlifting Performance and Endocrinological Responses
by Shyam Chavda, Angela Sorensen, James Vernau, Frank Hills, Chris Bishop and Anthony Nicholas Turner
Appl. Sci. 2025, 15(2), 748; https://doi.org/10.3390/app15020748 - 14 Jan 2025
Viewed by 1514
Abstract
Purpose: This study examined the acute performance-enhancing effects and endocrinological responses of a supramaximal clean pull performed at 120% of clean and jerk, one repetition maximum, on clean performance. Methods: Eight (n = 8) ranked collegiate level weightlifters attended two [...] Read more.
Purpose: This study examined the acute performance-enhancing effects and endocrinological responses of a supramaximal clean pull performed at 120% of clean and jerk, one repetition maximum, on clean performance. Methods: Eight (n = 8) ranked collegiate level weightlifters attended two days of testing in a randomised order. A control session was used to identify a baseline measure of kinetic and kinematic clean performance and endocrinological status following three cleans interspersed with one-minute recovery between repetitions. The experimental condition required participants to perform a single clean pull at 120% of clean and jerk, one repetition maximum, followed by three minutes recovery, prior to executing three cleans with one-minute recovery between repetitions. All cleans were performed on a dual force plate set up, synchronised with a 3D motion capture system to simultaneously record barbell and ground reaction force data. All endocrinological data were measured prior to the participant warming up and also following each testing protocol. Results: The results indicated that no significant differences were found between the control and PAP condition (p = 0.140–0.902); however, effect sizes from group analysis identified moderately negative to trivial effects across kinetic, kinematic and endocrinological variables (d = −0.30–0.14). Further analysis on an individual level demonstrated values, both negative and positive, ranging from extremely large (d = −4.10) to trivial (d = 0.04). Conclusions: The findings suggest a potentially negative affect of PAP on kinetic and kinematic measures of clean performance. However, individual responses varied, and thus some weightlifters may find this useful. Full article
(This article belongs to the Special Issue Advances in the Biomechanics of Sports)
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29 pages, 759 KiB  
Article
Linearized Harmonic Balance Method for Seeking the Periodic Vibrations of Second- and Third-Order Nonlinear Oscillators
by Chein-Shan Liu, Chung-Lun Kuo and Chih-Wen Chang
Mathematics 2025, 13(1), 162; https://doi.org/10.3390/math13010162 - 5 Jan 2025
Cited by 2 | Viewed by 1318
Abstract
To solve the nonlinear vibration problems of second- and third-order nonlinear oscillators, a modified harmonic balance method (HBM) is developed in this paper. In the linearized technique, we decompose the nonlinear terms of the governing equation on two sides via a constant weight [...] Read more.
To solve the nonlinear vibration problems of second- and third-order nonlinear oscillators, a modified harmonic balance method (HBM) is developed in this paper. In the linearized technique, we decompose the nonlinear terms of the governing equation on two sides via a constant weight factor; then, they are linearized with respect to a fundamental periodic function satisfying the specified initial conditions. The periodicity of nonlinear oscillation is reflected in the Mathieu-type ordinary differential equation (ODE) with periodic forcing terms appeared on the right-hand side. In each iteration of the linearized harmonic balance method (LHBM), we simply solve a small-size linear system to determine the Fourier coefficients and the vibration frequency. Because the algebraic manipulations required for the LHBM are quite saving, it converges fast with a few iterations. For the Duffing oscillator, a frequency–amplitude formula is derived in closed form, which improves the accuracy of frequency by about three orders compared to that obtained by the Hamiltonian-based frequency–amplitude formula. To reduce the computational cost of analytically solving the third-order nonlinear jerk equations, the LHBM invoking a linearization technique results in the Mathieu-type ODE again, of which the harmonic balance equations are easily deduced and solved. The LHBM can achieve quite accurate periodic solutions, whose accuracy is assessed by using the fourth-order Runge–Kutta numerical integration method. The optimal value of weight factor is chosen such that the absolute error of the periodic solution is minimized. Full article
(This article belongs to the Special Issue Computational Mathematics: Advanced Methods and Applications)
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23 pages, 23409 KiB  
Article
Seventh-Degree Polynomial-Based Single Lane Change Trajectory Planning and Four-Wheel Steering Model Predictive Tracking Control for Intelligent Vehicles
by Fei Lai and Chaoqun Huang
Vehicles 2024, 6(4), 2228-2250; https://doi.org/10.3390/vehicles6040109 - 23 Dec 2024
Viewed by 1193
Abstract
Single lane changing is one of the typical scenarios in vehicle driving. Planning a suitable single lane changing trajectory and tracking that trajectory accurately is very important for intelligent vehicles. The contribution of this study is twofold: (i) to plan lane change trajectories [...] Read more.
Single lane changing is one of the typical scenarios in vehicle driving. Planning a suitable single lane changing trajectory and tracking that trajectory accurately is very important for intelligent vehicles. The contribution of this study is twofold: (i) to plan lane change trajectories that cater to different driving styles (including aspects such as safety, efficiency, comfort, and balanced performance) by a 7th-degree polynomial; and (ii) to track the predefined trajectory by model predictive control (MPC) through four-wheel steering. The growing complexity of autonomous driving systems requires precise and comfortable trajectory planning and tracking. While 5th-degree polynomials are commonly used for single-lane change maneuvers, they may fail to adequately address lateral jerk, resulting in less comfortable trajectories. The main challenges are: (i) trajectory planning and (ii) trajectory tracking. Front-wheel steering MPC, although widely used, struggles to accurately track trajectories from point mass models, especially when considering vehicle dynamics, leading to excessive lateral jerk. To address these issues, we propose a novel approach combining: (i) 7th-degree polynomial trajectory planning, which provides better control over lateral jerk for smoother and more comfortable maneuvers, and (ii) four-wheel steering MPC, which offers superior maneuverability and control compared to front-wheel steering, allowing for more precise trajectory tracking. Extensive MATLAB/Simulink simulations demonstrate the effectiveness of our approach, showing improved comfort and tracking performance. Key findings include: (i) improved trajectory tracking: Four-wheel steering MPC outperforms front-wheel steering in accurately following desired trajectories, especially when considering vehicle dynamics. (ii) better ride comfort: 7th-degree polynomial trajectories, with improved control over lateral jerk, result in a smoother driving experience. Combining these two techniques enables safer, more efficient, and more comfortable autonomous driving. Full article
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