On an Optimal Linear Control Applied to a Non-Ideal Load Transportation System, Modeled with Periodic Coefficients

In this paper, a load transportation system in platforms or suspended by cables is considered. It is a monorail device and is modelled as an inverted pendulum built on a car driven by a DC motor. The governing equations of motion were derived via Lagrange's equations. In the mathematical model we consider the interaction between the DC motor and the dynamical system, that is, we have a so-called non-ideal periodic problem. The problem is analysed and we also developed an optimal linear control design to stabilize the problem.

Comments on energy confinement in non-periodic structures

In this study, we investigate the possibility of mode localization occurrence in a non-periodic Pfluger's column model of a rocket with an intermediate concentrated mass at its middle point. We discuss the effects of varying the intermediate mass magnitude and its position and the resulting energy confinement for two cases. Free vibration analysis and the severity of mode localization are appraised, without decoupling the system, by considering as a solution basis the fundamental free response or dynamical solution. This allows for the reduction of the dimension of the algebraic modal equation that arises from satisfying the boundary and continuity conditions. By using the same methodology, we also consider the case of a cantilevered Pluger's column with rotational stiffness at the middle support instead of an intermediate concentrated mass. (c) 2008 Elsevier Ltd. All rights reserved.

A reducing of a chaotic movement to a periodic orbit, of a micro-electro-mechanical system, by using an optimal linear control design

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

Parameter space for a dissipative Fermi-Ulam model

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

Stickiness in a bouncer model: A slowing mechanism for Fermi acceleration

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Nonlinear Dynamics and Control of an Ideal/Nonideal Load Transportation System With Periodic Coefficients

In this paper, a loads transportation system in platforms or suspended by cables is considered. It is a monorail device and is modeled as an inverted pendulum built on a car driven by a dc motor the governing equations of motion were derived via Lagrange's equations. In the mathematical model we consider the interaction between the dc motor and the dynamical system, that is, we have a so called nonideal periodic problem. The problem is analyzed, qualitatively, through the comparison of the stability diagrams, numerically obtained, for several motor torque constants. Furthermore, we also analyze the problem quantitatively using the Floquet multipliers technique. Finally, we devise a control for the studied nonideal problem. The method that was used for analysis and control of this nonideal periodic system is based on the Chebyshev polynomial exponsion, the Picard iterative method, and the Lyapunov-Floquet transformation (L-F transformation). We call it Sinha's theory.

On non-linear dynamics and a periodic control design applied to the potential of membrane action

The Fitzhugh-Nagumo (fn) mathematical model characterizes the action potential of the membrane. The dynamics of the Fitzhugh-Nagumo model have been extensively studied both with a view to their biological implications and as a test bed for numerical methods, which can be applied to more complex models. This paper deals with the dynamics in the (FH) model. Here, the dynamics are analyzed, qualitatively, through the stability diagrams to the action potential of the membrane. Furthermore, we also analyze quantitatively the problem through the evaluation of Floquet multipliers. Finally, the nonlinear periodic problem is controlled, based on the Chebyshev polynomial expansion, the Picard iterative method and on Lyapunov-Floquet transformation (L-F transformation).

The Yang-Lee zeros of the 1D Blume-Capel model on connected and non-connected rings

We carry out a numerical and analytic analysis of the Yang-Lee zeros of the ID Blume-Capel model with periodic boundary conditions and its generalization on Feynman diagrams for which we include sums over all connected and nonconnected rings for a given number of spins. In both cases, for a specific range of the parameters, the zeros originally on the unit circle are shown to depart from it as we increase the temperature beyond some limit. The curve of zeros can bifurcate- and become two disjoint arcs as in the 2D case. We also show that in the thermodynamic limit the zeros of both Blume-Capel models on the static (connected ring) and on the dynamical (Feynman diagrams) lattice tend to overlap. In the special case of the 1D Ising model on Feynman diagrams we can prove for arbitrary number of spins that the Yang-Lee zeros must be on the unit circle. The proof is based on a property of the zeros of Legendre polynomials.

Optimal Boussinesq model for shallow-water waves interacting with a microstructure

In this paper, we consider the propagation of water waves in a long-wave asymptotic regime, when the bottom topography is periodic on a short length scale. We perform a multiscale asymptotic analysis of the full potential theory model and of a family of reduced Boussinesq systems parametrized by a free parameter that is the depth at which the velocity is evaluated. We obtain explicit expressions for the coefficients of the resulting effective Korteweg-de Vries (KdV) equations. We show that it is possible to choose the free parameter of the reduced model so as to match the KdV limits of the full and reduced models. Hence the reduced model is optimal regarding the embedded linear weakly dispersive and weakly nonlinear characteristics of the underlying physical problem, which has a microstructure. We also discuss the impact of the rough bottom on the effective wave propagation. In particular, nonlinearity is enhanced and we can distinguish two regimes depending on the period of the bottom where the dispersion is either enhanced or reduced compared to the flat bottom case. © 2007 The American Physical Society.

Local attractors, degeneracy and analyticity: Symmetry effects on the locally coupled Kuramoto model

In this work we study the local coupled Kuramoto model with periodic boundary conditions. Our main objective is to show how analytical solutions may be obtained from symmetry assumptions, and while we proceed on our endeavor we show apart from the existence of local attractors, some unexpected features resulting from the symmetry properties, such as intermittent and chaotic period phase slips, degeneracy of stable solutions and double bifurcation composition. As a result of our analysis, we show that stable fixed points in the synchronized region may be obtained with just a small amount of the existent solutions, and for a class of natural frequencies configuration we show analytical expressions for the critical synchronization coupling as a function of the number of oscillators, both exact and asymptotic. © 2013 Elsevier Ltd. All rights reserved.

Periodicity in a delayed version of the kaldor trade cycle model

We are concerned with the Kaldor's trade cycle model under the effect of a delay which represents a gestation lag between a decision of investment and its effect on the capital stock. Taking the adjustment coefficient in the goods market as a bifurcation parameter, we achieve global branches of periodic solutions. In our setting the delay is a constant inherent to the specific economy. Copyright © 2013 Watam Press.

Statistical properties for a dissipative model of relativistic particles in a wave packet: A parameter space investigation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Molecular model for hydrated biological tissues

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

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)

A dissipative Fermi-Ulam model under two different kinds of dissipation

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