Some dynamical properties of a classical dissipative bouncing ball model with two nonlinearities

Some dynamical properties for a bouncing ball model are studied. We show that when dissipation is introduced the structure of the phase space is changed and attractors appear. Increasing the amount of dissipation, the edges of the basins of attraction of an attracting fixed point touch the chaotic attractor. Consequently the chaotic attractor and its basin of attraction are destroyed given place to a transient described by a power law with exponent -2. The parameter-space is also studied and we show that it presents a rich structure with infinite self-similar structures of shrimp-shape. © 2013 Elsevier B.V. All rights reserved.

Estudo de um depósito de argila ball clay de Tambaú (SP), para aplicação na indústria cerâmica de revestimentos

Pós-graduação em Geologia Regional - IGCE

The rolling ball problem on the plane revisited

By a sequence of rollings without slipping or twisting along segments of a straight line of the plane, a spherical ball of unit radius has to be transferred from an initial state to an arbitrary final state taking into account the orientation of the ball. We provide a new proof that with at most 3 moves, we can go from a given initial state to an arbitrary final state. The first proof of this result is due to Hammersley ( 1983). His proof is more algebraic than ours which is more geometric. We also showed that generically no one of the three moves, in any elimination of the spin discrepancy, may have length equal to an integral multiple of 2 pi.

A theoretical characterization of scaling properties in a bouncing ball system

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Instrumentação eletrônica para experimentação do modelo Bouncer Ball dissipativo

In our experiments, we studied the classical dynamic of a particle in vertical motion subject to a constant gravitational field and the partial shock with an elastic wall with oscillatory motion located below the particle. The motion of the particle was confined to the vertical direction by a glass guide tube, which was initially evacuated, allowing viscous drag forces to be disregarded. The time between impacts, as well as the time between the reference phase of the movement of the base and the moment of impact and the period of oscillation of the base will be acquired by a hardware and software to obtain the phases space to be compared later with the description of the system through mapping discrete variables via the 'particle velocity immediately after shock 'and' phase of the movement of the base at the instant of shock 'obtained by computer simulation. This requires developing an electronic analog system followed by Digital implemented in reconfigurable logic, more specifically a sequential machine able to discriminate the impact with the metal base from the impacts of the glass guide tube, based on the frequency spectrum of the response of the microphone to these different impacts

Effect of ball milling on the physicochemical characteristics of Peruvian carrot and cassava starches

Peruvian carrot and cassava starches were ground in a ball mill for 4, 8, 16, and 32 h and their structural and physicochemical characteristics were determined. Results obtained from HPAEC-PAD, GPC, and amylose content indicated a breaking of hydrogen bounds and α-(1 [RIGHTWARDS ARROW] 6) linkages of the starch molecules after treatment. X-ray diffractograms showed that the milling provided a reduction in the crystalline area of the starch granules. Most of the starch granules displayed agglomeration after 4 h of milling, when observed under a scanning electron microscope, and after 16 h a shapeless mass was observed for Peruvian carrot starch. Solubility and water absorption capacity of the starches increased with an increase in the milling time, while RVA profiles showed a progressive reduction of peak, breakdown, and final viscosities, as well as the development of initial viscosity. Gelatinization temperatures and enthalpies were reduced. Prolonged ball milling accelerated the enthalpy relaxation in both starches. These results confirmed a partial gelatinization of the starches, which was 82.6% for Peruvian carrot and 65.4% for cassava starches after 32 h of milling. The Peruvian carrot starch was more affected by the ball milling because of both its lower amylose content and the defects in its crystalline structure

Transport and dynamical properties for a bouncing ball model with regular and stochastic perturbations

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Global ballistic acceleration in a bouncing-ball model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Nonlinear ball and beam control system identification

The Ball and Beam system is a common didactical experiment in control laboratories that can be used to illustrate many different closed-loop control techniques. The plant itself is subjected to many nonlinear effects, which the most common comes from the relative motion between the ball and the beam. The modeling process normally uses the lagrangean formulation. However, many other nonlinear effects, such as non-viscous friction, beam flexibility, ball slip, actuator elasticity, collisions at the end of the beam, to name a few, are present. Besides that, the system is naturally unstable. In this work, we analyze a subset of these characteristics, in which the ball rolls with slipping and the friction force between the ball and the beam is non-viscous (Coulomb friction). Also, we consider collisions at the ends of the beam, the actuator consists of a (rubber made) belt attached at the free ends of the beam and connected to a DC motor. The model becomes, with those nonlinearities, a differential inclusion system. The elastic coefficients of the belt are experimentally identified, as well as the collision coefficients. The nonlinear behavior of the system is studied and a control strategy is proposed.

Dominant-non-dominant asymmetry of kicking a stationary and rolling ball in a futsal context

The aim of this study was to analyse the characteristics of the asymmetries in the dominant and non-dominant limbs when kicking stationary and rolling balls. Ten experienced Brazilian amateur futsal players participated in this study. Each participant performed kicks under two conditions (stationary ball vs. rolling ball) with the dominant and non-dominant limbs (five kicks per condition per limb). We analysed the kicking accuracy, ball and foot velocities, angular joint displacement and velocity. The asymmetry between the dominant and non-dominant limbs was analysed by symmetry index and two-way repeated measures ANOVA. The results did not reveal any interaction between the condition and limb for ball velocity, foot velocity and accuracy. However, kicking with the dominant limb in both kicks showed higher ball velocity (stationary ball: dominant - 24.27 ± 2.21 m · s(-1) and non-dominant - 21.62 ± 2.26 m · s(-1); rolling ball: dominant - 23.88 ± 2.71 m · s(-1) and non-dominant - 21.42 ± 2.25 m · s(-1)), foot velocity (stationary ball: dominant - 17.61 ± 1.87 m · s(-1) and non-dominant - 15.58 ± 2.69 m · s(-1); rolling ball: dominant - 17.25 ± 2.26 m · s(-1) and non-dominant - 14.77 ± 2.35 m · s(-1)) and accuracy (stationary ball: dominant - 1.17 ± 0.84 m and non-dominant - 1.56 ± 1.30 m; rolling ball: dominant - 1.31 ± 0.91 m and non-dominant - 1.97 ± 1.44 m). In addition, the angular joint adjustments were dependent on the limb in both kicks (the kicks with non-dominant limb showed lower hip external rotation than the kicks with the dominant limb), indicating that the hip joint is important in kick performance. In conclusion, the kicks with the non-dominant limb showed different angular adjustments in comparison to kicks with the dominant limb. In addition, kicking a rolling ball with the non-dominant limb showed higher asymmetry for accuracy, indicating that complex kicks are more asymmetric.