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The authors previously proposed a method to test different hypotheses concerning the human motor control strategies in a computationally efficient way. Its efficiency was demonstrated by modeling the human visual servoing of the 1D bouncing ball benchmark, which involves rhythmic interactions with the environment. Three candidate human-inspired control laws were discriminated based on their capacity to stabilize the task, as analyzed by means of Poincare maps. It was shown that the linear approximation, derived on these equilibrium points, of the human-like controller could be viewed as a state-feedback. Thus, the human-like controller was compared to the Linear Quadratic controller around the equilibrium point. The present study extends the analyzes made in this previous study by taking into account the influence of the arm and neural dynamics on the behavior adaptation to perturbations and task constraints. Particularly, the influence of these dynamics on the task stability is studied. Obtained results contribute to a better understanding of the human motor control strategies and will help to replicate these performances in robotics thanks to a more robust and less model-dependent robotic control architecture.

Human locomotion is similar to the motion of a bouncing ball. Therefore, the term “bouncing gait” has been used to describe locomotion in which the lower limbs perform the role of “springs” responsible for the movement of the general centre of mass. “Spring-mass model” is used to describe a bouncing gait and contains a material point that represents a total body mass and massless lower limb used as a “spring”, which performs the supporting function. An estimation of the stiffness of this spring determines the value of leg stiffness; this stiffness is a ratio of changes in the ground reaction force to the respective change in the “spring length” representing both lower limbs. Leg stiffness is a quantitative measure of elastic properties and determines the ability to accumulate potential elastic energy. The conceptual and methodological confusion regarding the concept of leg stiffness have made it difficult to organize and compare the results obtained by different authors. Due to the substantial roles of inertia and damping on force-displacement relationships, especially during transient states, leg stiffness in terms of human continuous movement should be considered as “quasi-stiffness”.

Understanding rates of change sets the foundations for differential equations that are central to modeling dynamic phenomena in science and engineering. While modeling with a constant rate of change is well understood, modeling an exponential change requires a more detailed approach due to a diversity of its computing. An exponential model can be characterized by a constant ratio of change of the quantity, a constant percent rate, decay or growth factor, decay or growth rate, and so forth. The purpose of this STEM activity was to create a STEM environment that would enable the learners to discover a constant ratio as a departing block to construct an exponential model. An experiment of investigating maximum heights of a bouncing ball was used as a scientific context. This phenomenon was selected due to providing observable and measurable data. A pretest analysis was used to identify students’ weaknesses, and the posttest analysis has been used to discuss students’ changes of perception on modeling exponential behavior. The STEM context has disclosed that the commonly applied term decay denoting a decreasing exponential function did not adequately describe the virtue of decaying processes. Conclusions and suggestions for further studies are discussed.

Particle damping is an emerging technology among passive devices for furnishing high damping of structural vibration, particularly in harsh environment, through the use of granular particles filled within an enclosure. In this work, we investigate experimentally the effect of acceleration amplitude, mass ratio, volume package, and type of material on the dynamic behavior of the particle damping to yield a thorough understanding of the attenuation mechanism played within such dampers. Experimental trials are realized within a rigid enclosure attached to a shaker and partially filled with particles. An analytical model based on the inelastic bouncing ball model (IBBM) is also developed in order to describe the nonlinear behavior of particle dampers. Our measurements reveal that the loss factor only relies on the total mass of the incorporated grains and on the driving magnitude. Further scaling of the loss factor, for all measurements, by the mass ratio led to a universal curve dependent only on the acceleration magnitude. A good agreement between the analytic model and the experimental results was verified.

In autonomous driving applications a critical challenge is to identify the action to take to avoid an obstacle on a collision course. For example, when a heavy object is suddenly encountered it is critical to stop the vehicle or change the lane even if it causes other traffic disruptions. However, there are situations when it is preferable to collide with the object rather than take an action that would result in a much more serious accident than collision with the object. For example, a heavy object which falls from a truck should be avoided whereas a bouncing ball or a soft target such as a foam box need not be.

The phase control is a well-known control method that has been typically applied to periodically driven dynamical systems. Its application allows controlling them through the phase difference between the forcing term and another harmonic perturbation. In the current chapter, we focus on the application of this control method to maps. In particular, we analyze two paradigmatic maps: the bouncing ball map and the Henon map. As a result, we observe that the application of the phase control can suppress or enhance the chaotic behavior on them. We also analyze the crisis induced intermittency in the bouncing ball map when the phase of the control signal is varied. Finally, the scaling behavior of the average Lyapunov exponents near the phase induced crisis is studied. Future applications of the phase control method are also discussed.

In this study, we developed an emotional virtual creature that grows according to a growth function model influenced by user input. Our preceding study proposed a growth model for emotions based on changes in the network structure of a self-organizing map. We applied a multilayer perceptron neural network to generate more sophisticated emotional expressions using growth functions. This model generated behavior similar to affective change, as described in behavioral genetics. Based on the growth model for emotions, we propose a virtual creature with which a user can interact using a tablet computer. This creature resembles a bouncing ball and changes color depending on its emotion. The user can pet or tap the creature, play with it using some items, and provide it food. The creature’s actions and emotional expressions are influenced by a various stimuli from the user. We implemented the virtual creature using an Apple iPad and confirmed that the creature grew and learned various emotional expressions through user interaction.

Duffing-Type Oscillators with Amplitude-Independent Period.- Asymptotics of Rigid-Body Motions for Nonlinear Dynamics: Physical In-sight and Methodologies.- Non-Linear Phenomena Exhibited by Flexible Cylindrical and Sector Shells.- Gear Shift Patterns in Uncertain Terrestrial Locomotion Systems.- Turbulence in Flexible Plates and Shells.- Using Bifurcation Diagrams for Controlling Chaos.- Shear Waves Dispersion in Cylindrically Structured Cancellous Viscoelastic Bones.- Quasi-Regular and Chaotic Dynamics of Postural Sway in Human.- Modeling of Ropes with Consideration of Large Deformations and Friction by Means of the Rigid Finite Element Method.- Dynamical Response of a Van Der Pol-Duffing System with an External Harmonic Excitation and Fractional Derivative.- Vortex Structure Around the Cylinder at a Flow of Viscous Fluid.- Asymptotic Analysis and Limiting Phase Trajectories in The Dynamics of Spring Pendulum.- Vibration Surveillance System with Variable Stiffness Holder for Flexible Details Milling.- Diversities in the Inverse Dynamics Problem for Underactuated Mechanical Systems Subject to Servo-Constraints.- Rare Phenomena and Chaos in Switching Power Converters.- Constrained Motion of Mechanical Systems and Tracking Control of Nonlinear Systems.- The General Conception of Intellectual Investigation the Regular and Chaotic Behavior of Dynamical Systems of Special Structure.- Dynamic Properties of Two-Axle Freight Wagon with UIC Double-Link Suspension as a Non-Smooth System with Dry Friction.- Dynamics of Mechanical Systems with Mecanum Wheels.- Reliability Analysis of the Dynamics of a Horizontal Drill-String.- Transition in Oscillatory Behavior in Mouse Oocyte and Mouse Embryo Trough Oscillatory Spherical Net Model of Mouse Zona Pellucida.- Constrained N-Body Problems.- Hunting French Ducks in Population Dynamics.- Model of Nonlinear Fractal Oscillator in Nanosystem.- Dynamical Statement Networks.- The Shooting Method for Non-Standard Boundary Value Problem.- Automatic Sleep Scoring From a Single Electrode Using Delay Differential Equations.- Methods for the Quick Analysis of Micro-Chaos.- Bouncing Ball Dynamics: Simple Motion of the Table Approximating the Sinusoidal Motion.- Periodic Motions of Coupled Oscillators Excited by Dry Friction and Harmonic Force.- Limit Cycle Oscillations of an Aerodynamic Pendulum.- Vibratory Energy Localization by Non-Smooth Energy Sink with Time-Varying Mass.- Coordinate-Free Formulation of Nonholonomic Constraints for Wheeled Robots.- Optomechatronic Choppers with Rotating Elements: Design Programs.- A Delay Mathematical Model for HIV Dynamics in HIV-Specific.- The Application of Parametric Excitation in Resonant MEMS Gyros.- Influence of Smart Materials on the Dynamical Response of Mechanical Oscillator.- Dynamical Pendulum-Like Nonconservative Systems.

We study nonlinear dynamics of a small ball moving vertically in a gravitational field and colliding with a moving table. Displacement of the table is approximated in one period of its motion by four cubic polynomials (we shall refer to this model as \(\mathcal{M}_{C}\)). The Poincare map, mapping a state of the ball at an impact to a new state at the next impact, is used to investigate the ball dynamics. Results obtained for the model \(\mathcal{M}_{C}\) are used to elucidate dynamics of the standard model of bouncing ball with sinusoidal motion of the limiter (model \(\mathcal{M}_{S}\)). Bifurcation diagrams are computed for the models \(\mathcal{M}_{C}\) and \(\mathcal{M}_{S}\). Then fixed points and their stability are determined for the \(\mathcal{M}_{C}\) model and compared with our earlier results for the model \(\mathcal{M}_{S}\). Finally, the birth of the low-velocity 2-cycle is investigated analytically for the \(\mathcal{M}_{C}\) model.