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An erratum published in the Journal of Applied Physics corrects a small mistake in the calculation of pendulum parameters in a previous work on impulse coupling measurement during laser ablation. The error affects values in Table III and several figures, but does not impact the overall conclusions of the study. The corrected figures and updated table of values are provided, showing a slight deviation between experimental and simulated results. [Extracted from the article]

Laser pulses were applied to a target mounted on a ballistic pendulum to study the momentum imparted by a laser shock impact. Photonic Doppler Velocimetry was used to assess the momentum imparted by each laser pulse. To increase the momentum produced, a layer of polymer transparent to the laser wavelength was applied to the surface of the targets to confine the plasma generated as a result of the laser–matter interaction. This yielded momentum coupling coefficients one hundred times higher than those obtained for equivalent laser parameters in the classical direct regime configuration. The study was completed by simulating the experiments with the one-dimensional Lagrangian hydrodynamics code ESTHER, which showed good agreement with the experimental results. [ABSTRACT FROM AUTHOR]

Laser ablation propulsion and orbit cleaning are developing areas of research. The general aim of laser-based techniques applied to this field is to maximize the momentum transfer produced by a laser shot. This work presents results from ballistic pendulum experiments under vacuum on aluminum, copper, tin, gold, and porous graphite targets. The work has focused on the metrology of the laser experiments to ensure good stability over a wide range of laser parameters (laser intensity ranging from 4 GW/cm 2 to 8.7 TW/cm 2 , pulse duration from 80 ps to 15 ns, and wavelengths of 528 or 1057 nm). The results presented compile data from three experimental campaigns spanning from 2018 to 2021 on two different laser platforms and using different pulse durations, energies, and wavelengths. The study is complemented by the simulation of the momentum from the mono-dimensional Lagrangian code ESTHER. The first part of this work gives a detailed description of the experimental setup used, the ESTHER code, and the treatment of the simulations. The second part focuses on the experimental results. The third part describes the simulation results and provides a comparison with the experimental data. The last part presents possible improvements for future work on the subject. [ABSTRACT FROM AUTHOR]

Aiming at the interferences caused by vibrations on the target monitoring system of satellite platforms, an experimental system of optical–mechanical–electrical joint image stabilization based on inertial sensors and piezoelectric fast mirrors was studied. First of all, the data from the fiber optic gyroscope and the detector are combined and processed. After that, the predicted intentional velocity is subtracted from the real-time gyroscope data, and the vibration displacement is obtained using an integral. The feedback amount is calculated using the processor according to the vibration displacement, the piezoelectric fast mirror is controlled to compensate the vibration interferences, and the purpose of stabilizing the images is achieved. The experimental results show that under a vibration interference of 300 μ rad /s, the image stabilization control frequency of the system reaches 500 Hz, the relative error between image frames is better than 3 μ rad , and the intra-frame stabilization performance of the detector meets the requirements on stabilized image and target detection for space targets on the star-carrying platform. [ABSTRACT FROM AUTHOR]

Synchronization is common in both nature and human physiology, often used to illustrate nonlinear dynamics. Interestingly, one can initiate their comprehension of this phenomenon from pure linear systems. In this Tutorial, we begin with a theoretical exploration of coupled oscillators' dynamic behavior, enabling us to discern and contrast the unique attributes of dissipative coupling as opposed to commonly observed coherent coupling. We then examine synchronization in two dissipative coupled linear systems: one with two pendulums mutually linked via the Lenz effect and the other with two RLC oscillators coupled via a resistor. This Tutorial is designed to serve as a concise starting point for researchers interested in exploring synchronization phenomena using a simplified model driven solely by dissipative coupling. [ABSTRACT FROM AUTHOR]

Friction pendulum bearings (FPBs) have emerged as critical structural isolation devices in the field of earthquake engineering. Extensive research and development efforts have led to the exploration and refinement of these bearings, resulting in the creation of various models with unique structural configurations and superior mechanical properties. This paper offers an in-depth review of the friction materials employed in FPBs, alongside an analysis of the mechanical performance and advancements in research regarding single-pendulum, double-pendulum, multiple-pendulum, and other types of friction bearings. Characterized by their low sensitivity and high stability, these bearings are adept at resisting seismic forces, thus providing dependable isolation protection for structures. This review also includes a succinct examination of the seismic performance and engineering applications of these isolation structures. With robust self-centering capabilities, excellent isolation, and energy dissipation mechanisms, FPBs are capable of quickly resuming normal operations post-seismic events. This reduces structural damage and maintenance expenses, significantly improving the seismic resilience of structures. Moreover, the paper outlines the current challenges in the research and development of FPBs and suggests future research directions, including optimizing friction materials, enhancing the design and performance of isolation structures, and improving the seismic performance and engineering application efficiency of FPBs. By identifying underexplored areas and synthesizing findings differently, this review provides a comprehensive and novel perspective that advances the field of earthquake engineering. [ABSTRACT FROM AUTHOR]

The paper delves into an in-depth analysis of the intrinsic resistance of the inverted pendulum system which causes the modeling of the system to differ from the actual system. Our primary objective revolves around the implementation and subsequent optimization of fuzzy logic controllers (FLC), drawing inspiration from human perceptual assessments. The processing comprises comprehensive mathematical system modeling, intrinsic resistance examination, and improved fuzzy logic control with detailed membership function and rule design. In addition, we conduct a comparative analysis with the widely recognized linear quadratic regulator (LQR) algorithm, which is considered the conventional control algorithm. The result demonstrates that the improved FLC outperforms the conventional LQR algorithm overshoot mitigation, thereby underscoring its superior efficacy and optimality. [ABSTRACT FROM AUTHOR]

Younger adults (YA) and older adults (OA) used a joystick to stabilize an unstable visual inverted pendulum (VIP) with a fundamental frequency (.27 Hz) of half that of bipedal human sway. Their task was to keep the VIP upright and to avoid ± 60° "fall" boundaries. Both age groups were tested with joystick gains and delays simulating age-related muscle strength and reflex slowing, respectively. In previous VIP and analogous self-balancing tasks, we observed a mixture of discrete corrective commands toward the balance point and destabilizing commands toward an impending fall. We hypothesized that (1) OA would fall more than YA, (2) traditional whole-trial stability and variability measures would differ across age groups and VIP conditions, and (3) different dynamics of corrective and destabilizing commands would discriminate falling from recovery. Results: (i) Traditional whole-trial performance metrics of fall incidence and the variance of position and velocity were worse in OA than YA and worse with longer delays and excessive joystick gains; (ii) OA made fewer corrective and more destabilizing commands than YA only when falling was imminent; (iii) when falls were imminent, a logistic model fit the percentage of inactive, corrective, and destabilizing commands as a function of time left to fall; and (iv) OA were like YA in switching between inaction and action, but exhibited less frequent and less prompt corrective commands than destabilizing commands relative to YA. We discuss whether such a decision-like process may also operate in a bipedal stance. [ABSTRACT FROM AUTHOR]

The primary goal of this work is to analyze the energized motion of three-degrees-of-freedom (3DOF) dynamic system consisting of a coupled double pendulum with the damped mass under the external harmonic forces and moments. Lagrangian equations are employed to derive the differential governing equations of motion (GEOM) based on the system generalized coordinates. The approximate solutions (AS) of these equations are generated through the utilization of the multiple scales technique (MST) at the third-order level of approximation. These solutions are ascertained by contrasting them with numerical solutions (NS) that are derived utilizing the fourth-order Runge-Kutta algorithm (RKA-4). The modulation equations are constructed, and the principal external resonance cases are scrutinized concurrently based on the solvability constraints. The steady-state solutions are studied. Based on Routh-Hurwitz criteria (RHC), the stability and instability zones are examined and assessed in the line with the steady-state solutions. The amplitudes and phases over a specific period of time have been graphed to illustrate the movement at any given instant. Furthermore, in order to evaluate the advantageous effects of different values pertaining to the physical parameters on the system behavior, the graphed representations of the obtained results, resonance reactions and areas of the stability are provided. The significance of the research model stems from its numerous applications such as the gantry cranes, robotics, pump compressors, transportation devices and rotor dynamics. It may be applied to the study of these systems' vibrational motion. [ABSTRACT FROM AUTHOR]

We consider two models of the predator–prey community with prey-taxis. Both models take into account the capability of the predators to respond to prey density gradients and also to one more signal, the production of which occurs independently of the community state (such a signal can be due to the spatiotemporal inhomogeneity of the environment arising for natural or artificial reasons). We call such a signal external. The models differ to one another through the description of their responses: the first one employs the Patlak–Keller–Segel law for both responses, and the second one employs Cattaneo's model of heat transfer for both responses following to Dolak and Hillen. Assuming a short-wave external signal, we construct the complete asymptotic expansions of the short-wave solutions to both models. We use them to examine the effect of the short-wave signal on the formation of spatiotemporal patterns. We do so by comparing the stability of equilibria with no signal to that of the quasi-equilibria forced by the external signal. Such an approach refers back to Kapitza's theory for an upside-down pendulum. The overall conclusion is that the external signal is likely not capable of creating the instability domain in the parametric space from nothing but it can substantially widen the one that is non-empty with no signal. [ABSTRACT FROM AUTHOR]

The walking ability of the elderly is a major global health concern. Most of the elderly experience walking difficulties such as decreased walking speed and loss of balance as well as coordination. To address this issue, a mechanical orthosis called the hip-knee-ankle-foot orthosis (HKAFO) has been designed to assist elderly individuals and hospital patients in performing therapeutic treatments. However, the existing standard HKAFOs have several limitations including high energy consumption and overloading of the hip and lower limb joints during walking activities. Therefore, this study aims to enhance the standard HKAFO by developing an electromechanical HKAFO (EM-HKAFO). The study involves developing a two-degree-of-freedom mathematical model of a double pendulum using Lagrange formulation to represent the HKAFO structure and evaluate the kinematic motions of the lower limbs. The performance of the proposed walking aid is evaluated using an actual instrumented EM-HKAFO focusing on its effectiveness in achieving a desired walking angle of 25°. The result indicates that the difference between simulation and experimental data is within an acceptable error range of 14%. Overall, this study contributes to the advancement of mobility aids and enhances the quality of life for elderly individuals and patients in need. [ABSTRACT FROM AUTHOR]

Background: This paper aims to complement the latest contribution in the literature that provides estimates of physiological parameters of a dynamic model for the elbow time profile during walking while linking them to a neurodegenerative disorder (Parkinsons's disease) characterized by motor symptoms. An upper limb model is here proposed in which an active contractile element is included within a model, viewing the arm as a double pendulum system and muscles as represented by a Kelvin–Voight system. All model parameters characterizing both the shoulder and the elbow of each subject are estimated via a gradient-like identifier whose exponential convergence properties are determined by a non-anticipative Lyapunov function, ensuring robustness features. Methods: Joint angle data from different walking subjects (healthy subjects and patients with Parkinson's disease) have been recorded using an IMU sensor system and compared with the joint angles obtained by means of the proposed model, which was adapted to each subject using available anthropometric knowledge and relying on the estimated parameters. Results: Experiments show that the reconstruction of shoulder and elbow time profiles can be definitely achieved through the proposed procedure with the estimated stiffness parameters turning out to constitute objective and quantitative indices of muscle stiffness (as a pivotal symptom of the pathology), which are able to track changes due to the therapy. Conclusions: The same dynamic model is actually able to capture the main features of the upper limb movement of both (healthy and pathological) walking subjects, with its parameters, in turn, characterizing the nature and progress of the pathology. [ABSTRACT FROM AUTHOR]

With advancements in bipedal locomotion for humanoid robots, a critical challenge lies in generating gaits that are bounded to ensure stable operation in complex environments. Traditional Model Predictive Control (MPC) methods based on Linear Inverted Pendulum (LIP) or Cart–Table (C-T) methods are straightforward and linear but inadequate for robots with flexible joints and linkages. To overcome this limitation, we propose a Flexible MPC (FMPC) framework that incorporates joint dynamics modeling and emphasizes bounded gait control to enable humanoid robots to achieve stable motion in various conditions. The FMPC is based on an enhanced flexible C-T model as the motion model, featuring an elastic layer and an auxiliary second center of mass (CoM) to simulate joint systems. The flexible C-T model's inversion derivation allows it to be effectively transformed into the predictive equation for the FMPC, therefore enriching its flexible dynamic behavior representation. We further use the Zero Moment Point (ZMP) velocity as a control variable and integrate multiple constraints that emphasize CoM constraint, embed explicit bounded constraint, and integrate ZMP constraint, therefore enabling the control of model flexibility and enhancement of stability. Since all the above constraints are shown to be linear in the control variables, a quadratic programming (QP) problem is established that guarantees that the CoM trajectory is bounded. Lastly, simulations validate the effectiveness of the proposed method, emphasizing its capacity to generate bounded CoM/ZMP trajectories across diverse conditions, underscoring its potential to enhance gait control. In addition, the validation of the simulation of real robot motion on the robots CASBOT and Openloong, in turn, demonstrates the effectiveness and robustness of our approach. [ABSTRACT FROM AUTHOR]

The classical problem of stabilization of the controlled inverted pendulum is considered in the case of stochastic perturbations of the type of Poisson's jumps. It is supposed that stabilized control depends on the entire trajectory of the pendulum. Linear and nonlinear models of the controlled inverted pendulum are considered, and the stability of the zero and nonzero equilibria is studied. The obtained results are illustrated by examples with numerical simulation of solutions of the equations under consideration. [ABSTRACT FROM AUTHOR]

Professor Richard Klein and his students built a bicycle with a rather interesting feature: no one was able to ride it. A prize was offered. Hundreds of students and cycling enthusiasts attempted it. Years passed, and the prize money grew. Klein's rear-steered bicycle became a canonical example of how non-minimum phase systems can be difficult and sometimes nearly impossible to control. It has been lauded as a particularly effective educational example in which students can experience the loss of controllability in a seemingly simple, albeit unorthodox bicycle. The primary result of the work reported here is a demonstration that it is possible for a human of modest athletic ability to ride Klein's unridable bicycle, to keep it balanced, and to control its direction of travel. There is a secret to riding Klein's rear-steer bicycle. The secret is revealed through an exploration of the dynamics and control of the bike that contains three elements: (1) modeling the physics of the actively steered bicycle as an inverted pendulum riding atop a carriage; (2) recognizing that the steer kinematics leads to competing physical mechanisms which an aspiring rider might exploit; and (3) examining limitations of controllability and stabilizability of the system from a state space perspective. From this vantage point, one can devise a novel strategy, based on a component of lateral acceleration that dominates at low speed, for riding the so-called "unridable" bike and solving Klein's puzzle. The work adds a new chapter on the dynamics and control of the rear-steered bicycle, a problem of academic interest. [ABSTRACT FROM AUTHOR]

In this paper, a novel adaptive safe fault-tolerant (SFT) controller design framework is proposed to obtain stability with safety guarantee for a class of single systems and a class of interconnected nonlinear systems in the presence of unknown faults. Under the framework, an adaptive fault-tolerant controller for a class of single systems is designed to ensure safety and asymptotic stability simultaneously. For interconnected systems, the neural networks (NNs) is used to parameterize the unknown faults and interconnection terms. Then, a necessary and sufficient condition for the stability of the system is relaxed and a certainty equivalence (CE)-based adaptive controller is proposed to reduce the complexity of control design. Finally, the result of input-to-state safety and uniform ultimate boundedness for the controlled interconnected systems can be obtained. A numerical simulation of the interconnected systems consisting of two inverted pendulums is given to illustrate the effectiveness of the proposed method. • For a class of single nonlinear systems with parameterized faults, an adaptive safe fault-tolerant control (SFT) law is proposed to ensure the asymptotic stability and safety of the systems. • The unsafe set is modified from a compact set to a bounded open set, which prevents the trajectory of the system state from sliding along the boundary of the unsafe set. • For a class of interconnected systems, a distributed adaptive SFT control design is further proposed based on the above method for single systems. To reduce the complexity of controller design, a certainty equivalence (CE)-based adaptive SFT control is presented. • This paper provides a new necessary and sufficient condition for the stability of the interconnected systems, which relaxes the original condition by removing the restriction on S set in Wang et al. (2020). [ABSTRACT FROM AUTHOR]

ABSTRACT A fixed‐time nonsingular terminal sliding mode control (TSMC) method based on emotional neural network (ENN) is proposed for nonlinear systems. First of all, a new terminal sliding surface (TSS) is proposed in this article, which can adaptively adjust when the system states are far and near the origin and achieve fixed time fast convergence. Second, the equivalent control term in the controller is approximated by the ENN, which solves the singularity problem of traditional TSMC and the problem of unknown model information simultaneously. Finally, by using Lyapunov stability theorem, it is proved that the system states are stable in a fixed time during both sliding and reaching stages, which is independent of the initial values. The proposed method is verified and compared on an inverted pendulum system, which shows a better control performance. [ABSTRACT FROM AUTHOR]

Since the occurrence of pedestrian-induced large lateral vibration of the London Millennium Bridge in 2000, scholars have realized the complexity of pedestrian-induced lateral vibrations. Despite extensive research spanning over two decades, the underlying mechanisms between pedestrians and footbridges remain incompletely understood. Currently, there are two main popular models for explaining the pedestrian-induced lateral vibration of the footbridge: the synchronization lock-in model and the self-excited force model. Among existing studies, the inverted pendulum model (IPM) essentially belongs to the self-excited force model, has gradually gained recognition. This model assumes that pedestrians maintain a constant step frequency and suggests that footbridge lateral vibration divergence can occur through pedestrian-bridge interaction without synchronization. Although the IPM theoretically elucidates the mechanism by which pedestrian-bridge interaction leads to self-excited forces, it still has its shortcomings: it overestimates the critical number of pedestrians required for triggering vibration divergence of the footbridge. The underlying cause of this problem stems from the inverted pendulum model’s inherent limitation as a single-mechanism framework, which fails to consider the adjustments of pedestrian’s step frequency and instead solely relies on the adjustments of pedestrian’s step width. Consequently, this results in an underestimation of the virtual equivalent damping coefficient that is in phase with the vibration velocity of the footbridge. This study proposes a generalized-inverted pendulum model (G-IPM), in which the pedestrian walking phase evolution is effectively combined with the IPM, thereby the adjustments of pedestrian’s step frequency and step width can be considered simultaneously. Compared to the single-mechanism-based IPM, the numerical simulation results indicate that the proposed dual-mechanism-based G-IPM requires fewer pedestrians to trigger the bridge vibration divergence, which is closer to the actual results. Additionally, parameter analysis reveals that varying pedestrian characteristic parameters exert different impacts on the vibration response of bridge. The proposed model pioneers the use of a dual-mechanism-based model, which is of significant theoretical importance in revealing the underlying mechanism of pedestrian-induced lateral vibrations of the footbridge. [ABSTRACT FROM AUTHOR]

Introduction: This paper aims at the control problem of nonlinear systems with uncertainty in general, and avoids the deviation of sliding mode controller from the preset constraint region during the convergence process. Methods: A sliding mode control method based on fuzzy adaptive technique was proposed by constructing obstacle Lyapunov function (BLF). Design problem of fuzzy adaptive second-order sliding mode controller considering output constraints. The Lyapunov function of the cutting barrier is designed, and the fuzzy adaptive second-order sliding mode controller is constructed by combining the Lyapunov function with the regression method. A second-order finite output sliding mode controller is designed for the inverted pendulum system. In the case of unknown external disturbance, the mathematical modeling and force analysis of the first order inverted pendulum system are carried out, and the design problem of the fuzzy adaptive second-order sliding mode controller with output restriction is studied. Results and Discussion: The proposed fuzzy adaptive second-order sliding mode controller has a good control effect in the inverted pendulum system. The fuzzy adaptive second-order controller stabilizes the sliding mode at 0.1 in 1.25 s, while the fuzzy adaptive second-order controller makes the system state reach equilibrium in 15 s. The accuracy of fuzzy adaptive second-order sliding mode controller reaches 99.2%, which is superior to other methods in terms of balance accuracy and recall rate. The controller not only has a fast response speed, but also can effectively suppress system flutter and ensure the rapid stability of the system after constraints. This research method lays a foundation for the design of fuzzy adaptive sliding mode control algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we study the number of zeros of Abelian integrals associated to some perturbed pendulum equations, and derive the new lower and upper bounds for the number of zeros of these integrals. The results we obtained correct some results of Theorem B and Proposition 1.1 in the paper (Gasull et al., 2016 [4]). [ABSTRACT FROM AUTHOR]

To a non-minimum phase nonlinear system, it was supposed that, if there is an output feedback control that stabilizes the auxiliary system, then there is an output feedback that stabilizes the original system. The existing methods base designing output feedback for non-minimum phase nonlinear system on the hypothesis that there exists output feedback for auxiliary system. However, the auxiliary system could be unobservable. Alternatively, this study aims to create a way to design output feedback for auxiliary systems in unobservable situation. An output state is constructed in the last equation of auxiliary system, which artificially makes the internal dynamics of the auxiliary system observable. Then, a cascade high-gain observer is designed for the auxiliary system, consisting of an extended high-gain observer for external dynamics and a high-gain observer for internal dynamics of the auxiliary system. Therefore, the output feedback control for auxiliary system can be designed via the cascade high-gain observer and a state feedback. Finally, the proposed method is demonstrated by an academic example and an inverted pendulum on a cart in the simulation. [ABSTRACT FROM AUTHOR]

This paper presents a tutorial-style approach to synthesizing a mechatronic control system from scratch, with a focus on mathematical modeling, real-world verification, model-based control using the Linear Quadratic Regulator (LQR), and rapid control prototyping. The system's equations of motion are derived through Lagrangian mechanics and subsequently linearized. Unknown parameters are estimated using optimization techniques. An LQR controller is designed and implemented on the STM32F4 microcontroller and its performance is rigorously tested against disturbances using MATLAB/Simulink. The Reaction Wheel Pendulum serves as the case study, demonstrating the successful implementation of the LQR controller, with the derived model verified through experimentation. A recovery angle of 20 degrees is obtained. [ABSTRACT FROM AUTHOR]

Farmers in North America face significant pressure from insects in their maize fields, particularly from corn rootworm (Diabrotica spp.). Research into proteins capable of insecticidal activity has found several produced by ferns. One protein, IPD079Ea, was derived from Ophioglossum pendulum and has shown activity against corn rootworm. An environmental risk assessment was conducted for maize event DP-915635-4, which provides control of corn rootworms via expression of the IPD079Ea protein. This assessment focused on IPD079Ea and characterized potential exposure and hazard to non-target organisms (NTOs). For exposure, estimated environmental concentrations (EECs) were calculated. For hazard, laboratory dietary toxicity studies were conducted with IPD079Ea and surrogate non-target organisms. Environmental risk was characterized by comparing hazard and exposure to calculate the margin of exposure (MOE). Based on the MOE values for DP-915635-4 maize, the IPD079Ea protein is not expected to result in unreasonable adverse effects on beneficial NTO populations at environmentally relevant concentrations. [ABSTRACT FROM AUTHOR]

In this research, I advance an interpretation of Machiavelli's philosophy for constitutional change. I suggest that Machiavelli's reading of Polybius's theory of anacyclosis (circular theory of political change) opens up a new vision for political action and historical transformation. Machiavelli subjects the inherited metaphysical conception of constitutional change to a secular view, one characterized by virtue of action and uncertainty of outcomes (Virtù/Fortuna), social divisions (nobility/plebeians), and political ideals (Republicanism). The interpretive suggestion put forth here is that Machiavelli's innovation of the ancient theory of constitutional changes can be appreciated in terms of an oscillating pendulum rather than as a cycle, thereby fictitiously referring to the pendulum as an instrument mimicking the 'truth of the matter' (verità effettuale) of a perpetual shift between principalities and republics rather than as an esoteric rite to foresee the future. [ABSTRACT FROM AUTHOR]

Earlier, an approximation technique was presented for solving strong nonlinear oscillator equations. Due to arising algebraic complexities, the method fails to determine suitable solutions of some nonlinear oscillators such as quadratic oscillators, the cubical Duffing oscillator of softening springs, and pendulum equations. Then, rearranging an algebraic equation related to amplitude and frequency, the method covers the noted problems. In this article, the latter technique is applied to handling anti-symmetric constant force oscillators and anti-symmetric quadratic nonlinear oscillators. [ABSTRACT FROM AUTHOR]

We discuss different approaches for the analytical description of a mechanical system used in control theory, aiming at the analytical modelling of experimental artefacts observed in the implementation of ideal searched trajectories. Starting from an established analytical solution, we develop an alternative analytical model for this solution with minimal deviations and then extend this starting point to a more flexible toolbox that incorporates a variety of phenomena that typically occur in real implementations of this mechanical system, thus providing an important step towards bridging the gap between theoretical models and experimental reality. [ABSTRACT FROM AUTHOR]

The precise movement of the test mass along a geodesic is crucial for gravitational wave detection in space. To maintain this motion, the core payload-inertial sensor incorporates multiple functional units designed to mitigate various sources of stray force noise affecting the test mass. Understanding the limits of these noise sources is essential for enhancing the inertial sensor system design. Additionally, thorough ground-based verification of these functional units is necessary to ensure their reliability for space missions. To address these challenges, we developed a low-frequency torsion pendulum apparatus that utilizes a commercial autocollimator as the optical readout element for testing this type of space inertial sensor. This paper provides a comprehensive overview of the apparatus's operating principle, structural characteristics, and the results of laboratory tests of its background noise. Experimental data demonstrate that the torsion pendulum achieves a sensitivity of 1 × 10−11 Nm/Hz1/2 within the measurement band from 1 mHz to 0.1 Hz, confirming its suitability for various inertial sensor tests. Furthermore, the insights gained from constructing the torsion pendulum will inform future system upgrades. [ABSTRACT FROM AUTHOR]

Runway surface friction is critically important to safe aircraft operations and mostly depends on the surface texture, which provides grip in the presence of contamination and directly affects the friction coefficient in general. Microtexture assessment is the most challenging part of texture assessment since there is no standardised pavement microtexture control method in runway maintenance and management practice. The purpose of this study was to develop a simple laser profilometer and analysis model and subsequent validation for use in runway friction surveys. To that end, a simple laser profilometer was developed, and a profile picture analysis and macrotexture filtration method were designed. Test results were compared to the stylus-based roughness tester and the British Pendulum Tester. The proposed profile picture analysis and profile smothering and filtration methodology, based on linear approximation, is simpler and more effective for the case of macrotexture filtration for the friction survey. The laser profilometer model results were highly correlated with the stylus-based roughness tester results (R2 = 0.99). The average roughness of the microtexture profile, after smothering and macrotexture filtration, also showed good correlation with the British Pendulum results (R2 = 0.78). The results from this study confirm the possibility of texture assessment for routine runway friction surveys using a simple and economical laser profilometer, which is not routinely available in current airport surface friction management. [ABSTRACT FROM AUTHOR]

We present a model-based feedforward control strategy suitable for designing swift rest-to-rest maneuvers for liquids in arbitrarily shaped containers. We employ the commonly used equivalent pendulum model to represent the sloshing dynamics and suggest a novel parameter identification scheme suitable for arbitrary container shapes and any number of sloshing modes. By computing natural modes and fluid reaction forces and torques for imposed harmonic container motions via a finite element model, we obtain data for the identification scheme. A fitting procedure then yields highly accurate parameters for a physical pendulum model, where each pendulum represents one sloshing mode. We also provide a thorough analysis of parameter identifiability and guidelines for obtaining robust parameter estimates. The proposed feedforward control method uses a virtual tray pendulum on which we place the container (in the form of its equivalent pendulum model). Designing the virtual tray such that the fluid's dominant sloshing mode cannot be excited by horizontally moving the tray pendulum pivot effectively zeros out any sloshing motion in this mode. We then exploit the flatness property of the resulting system to design rest-to-rest maneuvers where any residual sloshing motion (in higher modes) can be exactly stopped at the end of the maneuver. The effectiveness of the proposed method is demonstrated through extensive simulations and experimental results using a Martini cocktail glass, whose shape is challenging in terms of sloshing. The experimental results show the successful, accurate suppression of sloshing, validating the efficacy of the proposed concept. [ABSTRACT FROM AUTHOR]

Data-Driven Response Regime Exploration and Identification (DR 2 EI) is a novel and fully data-driven method for identifying and classifying response regimes of a dynamical system without requiring human intervention. This approach is a valuable tool for exploring and discovering response regimes in complex dynamical systems, especially when the governing equations and the number of distinct response regimes are unknown, and the system is expensive to sample. Additionally, the method is useful for order reduction, as it can be used to identify the most dominant response regimes of a given dynamical system. DR 2 EI utilizes unsupervised learning algorithms to transform the system's response into an embedding space that facilitates regime classification. An active sequential sampling approach based on Gaussian Process Regression is used to efficiently sample the parameter space, quantify uncertainty, and provide optimal trade-offs between exploration and exploitation. The performance of the DR 2 EI method was evaluated by analyzing three established dynamical systems: the mathematical pendulum, the Lorenz system, and the Duffing oscillator, and its robustness to noise was validated across a range of noise magnitudes. The method was shown to effectively identify a variety of response regimes with both similar and distinct topological features and frequency content, demonstrating its versatility in capturing a wide range of behaviors. While it may not be possible to guarantee that all possible regimes will be identified, the method provides an automated and efficient means for exploring the parameter space of a dynamical system and identifying its underlying "sufficiently dominant" response regimes without prior knowledge of the system's equations or behavior. [ABSTRACT FROM AUTHOR]

This article researches the issue of robust non-fragile hybrid control for delayed uncertain singular impulsive jump systems (USIMJSs). The key aim is to design non-fragile hybrid state feedback controllers (including a non-fragile normal state feedback controller and a non-fragile impulsive state feedback controller), which are insensitive to the uncertainties of gains of controllers and can provide sufficient tuning margins. The non-fragile normal state feedback controller can eliminate the internal impulses and overcome the external disturbances; the non-fragile impulsive state feedback controller can suppress the interference of external unstable impulses and restrain the instantaneous jumps caused by Markovian modes switching. By introducing impulse instant-dependent auxiliary functions, the improved impulse-time-dependent Lyapunov–Krasovskii functional is constructed, which can capture the information of the impulse instants and Markovian jump modes. Novel criteria of robust admissibilization for delayed USIMJSs are acquired under linear matrix inequalities framework. Lastly, the effectiveness of the derived algorithm and designed method is confirmed by simulation examples including a direct current motor-controlled inverted pendulum device and a Quarter-Car active suspension model. • The non-fragile hybrid state feedback controllers (NFHSFC, including a NSFC and an ISFC) are designed. • The impulse instant-dependent auxiliary functions are introduced to construct the improved L–K functional. • The proposed NFHSFC method is more universal, regularity and non-impulsiveness need not be assumed in advance. [ABSTRACT FROM AUTHOR]

In this paper, we address the modeling, simulation, and control of a rotary inverted pendulum (RIP). The RIP model assembled via the MATLAB (Matlab 2021a)®/Simulink (Simulink 10.3) Simscape (Simscape 7.3)™ environment demonstrates a high degree of fidelity in its capacity to capture the dynamic characteristics of an actual system, including nonlinear friction. The mathematical model of the RIP is obtained via the Euler–Lagrange approach, and a parameter identification procedure is carried out over the Simscape model for the purpose of validating the mathematical model. The usefulness of the proposed Simscape model is demonstrated by the implementation of a variety of control strategies, including linear controllers as the linear quadratic regulator (LQR), proportional–integral–derivative (PID) and model predictive control (MPC), nonlinear controllers such as feedback linearization (FL) and sliding mode control (SMC), and artificial intelligence (AI)-based controllers such as FL with adaptive neural network compensation (FL-ANC) and reinforcement learning (RL). A design methodology that integrates RL with other control techniques is proposed. Following the proposed methodology, a FL-RL and a proportional–derivative control with RL (PD-RL) are implemented as strategies to achieve stabilization of the RIP. The swing-up control is incorporated into all controllers. The visual environment provided by Simscape facilitates a better comprehension and understanding of the RIP behavior. A comprehensive analysis of the performance of each control strategy is conducted, revealing that AI-based controllers demonstrate superior performance compared to linear and nonlinear controllers. In addition, the FL-RL and PD-RL controllers exhibit improved performance with respect to the FL-ANC and RL controllers when subjected to external disturbance. [ABSTRACT FROM AUTHOR]

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For the problem of control of flexible linear double inverted pendulum (FLDIP), considering that the method of obtaining LQR parameters through traditional manual trial-and-error is too cumbersome, and the basic particle swarm optimization algorithm has a slower convergence speed and is prone to a local optimal solution, in this paper, a control method is proposed that it can achieve autonomous optimization based on improved the particle swarm optimization (PSO) algorithm. Firstly, the mathematical model of the FLDIPs is given to analyse the stability of the system. Then, the PSO algorithm is improved from the perspective of dynamically adjusting inertia weights to optimize linear quadratic regulator (LQR) parameters. Finally, through simulation comparison with the LQR control effect obtained by the manual trial and error method, the feasibility of the improved PSO algorithm is verified. This method can not only improve the control performance of the system but also effectively overcome the problem of blindness in selecting Q for traditional LQR optimal control. [ABSTRACT FROM AUTHOR]

This article presents a reactive planning and control framework to enhance the robustness of humanoid robots locomotion against external disturbances. The framework comprises two main modules, reactive planning and motion optimization. In the reactive planning module, a reactive footstep compensation strategy based on the essential motion of the linear inverted pendulum model (LIPM) is proposed. This strategy leverages the periodic motion characteristics of the LIPM, deriving the correct footstep compensation based on the conditions for model stability restoration. The module generates the zero moment point planning trajectories based on the footstep compensation. In the motion optimization module, motion optimization based on reactive planning is performed. To make motion constraint based on capture point applicable to motion optimization, the impact of different truncation points on stability constraints to determine the appropriate truncation point is quantified. The effectiveness of the proposed framework is demonstrated through experiments conducted on the humanoid robot UBTECH Walker2. [ABSTRACT FROM AUTHOR]

Purpose: Relational contracting is increasingly being applied to complex and uncertain construction projects. However, it has proved hard to achieve stable performance and industry-level learning in this field. This paper employs an institutional perspective to analyze how legitimacy for relational contracting has been produced and challenged in Denmark, Finland, Norway and Sweden, including implications for dissemination and learning. Design/methodology/approach: A collaborative case study design is used, where longitudinal accounts of the developments in relational contracting over more than 25 years in four Nordic countries were developed by scholars based in each country. The descriptions are underpinned by literature sources from research, practice and policy. Findings: The countries share similar problem perceptions that have triggered the de-institutionalization of traditional contracting practices. Models and policies developed elsewhere are important sources of knowledge and legitimacy. Most countries have seen pendulum movements, where dissemination of relational contracting is followed by backlashes when projects fail to meet projected outcomes. Before long, however, relational contracting tends to re-emerge under new labels and in slightly new forms. Such a proliferation of concepts presents further obstacles to learning. Successful institutionalization is found to rely on realistic goals in combination with broad competence development at the organizational and industry levels. Practical implications: In seeking inspiration from other countries, policymakers should go beyond contract models to also consider strategies to manage industry-level learning. Originality/value: The paper provides a unique longitudinal cross-country perspective on the field of relational contracting. As such, it contributes to the small stream of literature on long-term institutional change in the construction sector. [ABSTRACT FROM AUTHOR]

It has been widely confirmed that symmetry can lead to synchronization. However, it is also evident that synchronization or cluster synchronization phenomena commonly occur in asymmetric networks. In this article, we study the Hopf bifurcation of anti-synchronous periodic solutions in a class of asymmetric coupled oscillator systems. In contrast to symmetric synchronous systems, e.g., pendulums with Huygens' coupling, oscillators in ring networks, neurons in mirror symmetric networks, the systems we investigated exhibit anti-synchronous periodic solutions that do not align with their symmetry. Due to the absence of symmetry in these systems, the simultaneous diagonalization between the Jacobi matrix of equilibrium and the rotating matrix representing the types of synchronous solutions is mathematically impossible. This introduces greater complexity in the analysis of dynamics. The main innovation of this paper is to establish the Hopf bifurcation of the rotating periodic solutions for such asymmetric systems. By demonstrating the bifurcation of anti-synchronous periodic solutions in two coupled oscillator systems with three and four oscillators, corresponding to whether the Jacobi matrix of the system is semi-simple, we illustrate the validity of our method. [ABSTRACT FROM AUTHOR]

This essay proposes that the only publication of the Accademia del Cimento, referred to as Saggi,11 Accademia del Cimento, Saggi di naturali esperienze fatte nell’ Accademia del Cimento sotto la protezione del serenissimo principe Leopoldo di Toscana e descritte dal segretario di essa Accademia (Firenze: Per Giuseppe Cocchini, 1667). had as one of its main goals the celebration of the House of Medici’s paternity of cutting-edge experiments and instruments during the reign of Grand Duke Ferdinando II. These included Ferdinando II’s thermometers and hygrometers, Torricelli’s experiment and barometer, and Galileo’s pendulum as a clock-regulator. It seems that this agenda went unnoticed, not at the time of its initial circulation, but rather in modern historiography. Christiaan Huygens’s challenged invention of the pendulum clock provides a case study to explore the agenda of this publication and the problem of defining an invention in seventeenth-century Europe. This paper presents for the first time the document that attests to when the first specimen of Huygens’s clock arrived in Florence, disproving the previously believed date of September 1657. The paper argues that over the last two centuries, this error has made the Medici narratives of this dispute appear inconsistent and marginalized them. In light of this new find, they must be reconsidered.Accademia del Cimento, Saggi di naturali esperienze fatte nell’ Accademia del Cimento sotto la protezione del serenissimo principe Leopoldo di Toscana e descritte dal segretario di essa Accademia (Firenze: Per Giuseppe Cocchini, 1667). [ABSTRACT FROM AUTHOR]

In electromechanical systems, backlash in gear trains can lead to a degradation in control performance. We propose a drive–anti-drive mechanism to address this issue. It consists of two DC motors that operate in opposite directions. One motor acts as the drive, while the other serves as the anti-drive to compensate for the backlash. This work focuses on switching between the drive and anti-drive motors, controlled by a switched-mode PID controller. Simulation results on an inverted pendulum demonstrate that the proposed scheme effectively compensates for backlash, improving position accuracy and control. This switched controller approach enhances the performance of electromechanical systems, particularly where gear backlash poses challenges to closed-loop performance. [ABSTRACT FROM AUTHOR]

This article investigates the finite‐time (FT) boundedness problem for the time delay (TD) Takagi–Sugeno fuzzy model (TSFM) with conformable derivative (CD) and in the presence of certain actuator faults. Through the reconstruction of an appropriate Lyapunov–Krasovskii functional, some sufficient conditions expressed by the linear matrix inequalities (LMIs) are given to ensure the FT boundedness of the proposed model not only during regular operation but also when encountering certain actuator faults. Finally, a numerical example and an inverted pendulum system are presented to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we consider the bifurcation of small-amplitude limit cycles near the origin in perturbed pendulum systems of the form x ˙ = y , y ˙ = − sin ⁡ (x) + ε Q (x , y) , where Q (x , y) is a smooth or piecewise smooth polynomial in the triple (sin ⁡ (x) , cos ⁡ (x) , y) with free coefficients. We obtain sharp upper bounds on the number of positive zeros of its associated first order Melnikov function near h = 0 for Q (x , y) being smooth and piecewise smooth with the discontinuity at y = 0 or x = 0 , respectively. [ABSTRACT FROM AUTHOR]

Template models, such as the Bipedal Spring-Loaded Inverted Pendulum and the Virtual Pivot Point, have been widely used as low-dimensional representations of the complex dynamics in legged locomotion. Despite their ability to qualitatively match human walking characteristics like M-shaped ground reaction force (GRF) profiles, they often exhibit discrepancies when compared to experimental data, notably in overestimating vertical center of mass (CoM) displacement and underestimating gait event timings (touchdown/ liftoff). This paper hypothesizes that the constant leg stiffness of these models explains the majority of these discrepancies. The study systematically investigates the impact of stiffness variations on the fidelity of model fittings to human data, where an optimization framework is employed to identify optimal leg stiffness trajectories. The study also quantifies the effects of stiffness variations on salient characteristics of human walking (GRF profiles and gait event timing). The optimization framework was applied to 24 subjects walking at 40% to 145% preferred walking speed (PWS). The findings reveal that despite only modifying ground forces in one direction, variable leg stiffness models exhibited a >80% reduction in CoM error across both the B-SLIP and VPP models, while also improving prediction of human GRF profiles. However, the accuracy of gait event timing did not consistently show improvement across all conditions. The resulting stiffness profiles mimic walking characteristics of ankle push-off during double support and reduced CoM vaulting during single support. [ABSTRACT FROM AUTHOR]

In this article, the solutions of Bessel's differential equations (DEs) by variable change method are formulated. To do so, we have considered the first and second kind of Bessel's functions which are obtained as solutions of Bessel's equations and it is used to determine the solutions of the lengthening pendulum (LP). To solve the given equations, we have used Frobenius theorem and the gamma function and hence, apply the obtained results to solve the LP. The finding reveals that Bessel's functions establish the solutions of LP equations. The solutions obtained for lengthening the pendulum are illustrated graphically using the computer software of MathLab. The graphical results show that the sinusoidal wave natures are compressed or extended based on the chosen parameter k. Finally, it is concluded that the obtained method gives an effective, efficient, and systematic method. [ABSTRACT FROM AUTHOR]

For a pendulum suspended below a vibrating block with white noise forcing, the solution in which the pendulum remains vertical is called the single mode solution. When this solution becomes unstable there is energy transfer from the block to the pendulum, helping to absorb the vibrations of the block. We study the Lyapunov exponent λ governing the almost-sure stability of the process linearized along the single mode solution. The linearized equation is excited by a combination of white and colored noise processes, which makes the evaluation of λ nontrivial. Depending on the relative sizes of the noise intensity and the damping coefficients, λ may take either negative or positive values. For white noise forcing of intensity εν we prove λ(ε) =λ0+ε²λ2+O(ε4) as ε →0, where λ0 and λ2 are given explicitly in terms of the parameters of the system. [ABSTRACT FROM AUTHOR]

The paper presents output feedback control of a class of two-time-scale nonlinear systems. State feedback control for two-time-scale system is converted into output feedback via two high-gain observers. The high-gain observers are designed for reduced-order, quasi-steady-state, and boundary layer models of the two-time-scale system. Analyses reveal three-time-scale structure of the closed-loop system. Convergence of the closed-loop system is guaranteed under sufficient conditions. Simulation results of control of inverted pendulum on a cart illustrate the application of the proposed methodology. [ABSTRACT FROM AUTHOR]