On local analysis of oscillations of a non-ideal and non-linear mechanical model

It is of major importance to consider non-ideal energy sources in engineering problems. They act on an oscillating system and at the same time experience a reciprocal action from the system. Here, a non-ideal system is studied. In this system, the interaction between source energy and motion is accomplished through a special kind of friction. Results about the stability and instability of the equilibrium point of this system are obtained. Moreover, its bifurcation curves are determined. Hopf bifurcations are found in the set of parameters of the oscillating system.

Swarm Control Designs applied to a Mechanical Oscillator

This paper presented the particle swarm optimization approach for nonlinear system identification and for reducing the oscillatory movement of the nonlinear systems to periodic orbits. We analyzes the non-linear dynamics in an oscillator mechanical and demonstrated that this model has a chaotic behavior. Chaos control problems consist of attempts to stabilize a chaotic system to an equilibrium point, a periodic orbit, or more general, about a given reference trajectory. This approaches is applied in analyzes the nonlinear dynamics in an oscillator mechanical. The simulation results show the identification by particle swarm optimization is very effective.

Stability results for impulsive functional differential equations with infinite delay

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

Viabilidade econômica para produção de mel em propriedade familiar

Em 2009, o Brasil quebrou o seu recorde de exportação de mel, gerando receita superior a US$ 65 milhões. Entretanto, existe uma lacuna nos aspectos econômicos, para grande parte dos apicultores inseridos nesta cadeia. Desta forma, levantou-se o investimento necessário para a produção de mel, em uma propriedade familiar de Cajuru (SP), com estimativas de investimento e custos de produção baseados no Custo Operacional Total (COT) utilizado pelo Instituto de Economia Agrícola, obtendo-se R$ 97.093,00 como valor total do investimento. Para a análise econômica, avaliando-se a produção de mel originária de flor de laranjeira e silvestre, o custo operacional total foi de R$ 16.400,13, considerando-se que as despesas com insumos perfizeram 70% do Custo Operacional Efetivo (COE) e 26% do COT, obtendo-se índice de lucratividade de 46%. em relação ao ponto de nivelamento, o apicultor precisa produzir 4.659 kg de mel, ou vender ao preço mínimo de R$ 1,93/kg a produção obtida, para cobrir os custos. Constatou-se, com base no fluxo de caixa, TIR de 7,24% e que o investimento inicial retorna em 10 anos, mostrando resultados atrativos para este segmento agropecuário, considerando-se a racionalidade de uso dos fatores de produção, bem como um aumento progressivo na quantidade produzida.

Alternative paths for insertion of probes into high inclination lunar orbits

The dynamics of the restricted three-body Earth-Moon-particle problem predicts the existence of direct periodic orbits around the Lagrangian equilibrium point L1. From these orbits, we derive a set of trajectories that form links between the Earth and the Moon and are capable of performing transfers between terrestrial and lunar orbits, in addition to defining an escape route from the Earth-Moon system. When we consider a more complex and realistic dynamical system - the four-body Sun-Earth-Moon-particle (probe) problem - the trajectories have an expressive gain of inclination when they penetrate in the lunar influence sphere, thus allowing the insertion of probes into low-altitude lunar orbits with high inclinations, including polar orbits. In this study, we present these links and investigate some possibilities for performing an Earth-Moon transfer based on these trajectories. (C) 2007 COSPAR. Published by Elsevier Ltd. All rights reserved.

Blood glucose responses in humans mirror lactate responses for individual anaerobic threshold and for lactate minimum in track tests

The equilibrium point between blood lactate production and removal (La-min(-)) and the individual anaerobic threshold (IAT) protocols have been used to evaluate exercise. During progressive exercise, blood lactate [La-](b), catecholamine and cortisol concentrations, show exponential increases at upper anaerobic threshold intensities. Since these hormones enhance blood glucose concentrations [Glc](b), this study investigated the [Glc] and [La-](b) responses during incremental tests and the possibility of considering the individual glucose threshold (IGT) and glucose minimum;(Glc(min)) in addition to IAT and La-min(-) in evaluating exercise. A group of 15 male endurance runners ran in four tests on the track 3000 m run (v(3km)); IAT and IGT- 8 x 800 m runs at velocities between 84% and 102% of v(3km); La-min(-) and Glc(min) - after lactic acidosis induced by a 500-m sprint, the subjects ran 8 x 800 m at intensities between 87% and 97% of v(3km); endurance test (ET)- 30 min at the velocity of IAT. Capillary blood (25 mu l) was collected for [La-](b) and [Glc](b) measurements. The TAT and IGT were determined by [La-](b) and [Glc](b) kinetics during the second test. The La-min(-) and Glc(min) were determined considering the lowest [La-] and [Glc](b) during the third test. No differences were observed (P < 0.05) and high correlations were obtained between the velocities at IAT [283 (SD 19) and IGT 281 (SD 21)m. min(-1); r = 0.096; P < 0.001] and between La,, [285 (SD 21)] and Glc(min) [287 (SD 20) m. min(-1) = 0.77; P < 0.05]. During ET, the [La-](b) reached 5.0 (SD 1.1) and 5.3 (SD 1.0) mmol 1(-1) at 20 and 30 min, respectively (P > 0.05). We concluded that for these subjects it was possible to evaluate the aerobic capacity by IGT and Glc(min), as well as by IAT and La-min(-).

Reversible equivariant Hopf bifurcation

In this paper we study codimension-one Hopf bifurcation from symmetric equilibrium points in reversible equivariant vector fields. Such bifurcations are characterized by a doubly degenerate pair of purely imaginary eigenvalues of the linearization of the vector field at the equilibrium point. The eigenvalue movements near such a degeneracy typically follow one of three scenarios: splitting (from two pairs of imaginary eigenvalues to a quadruplet on the complex plane), passing (on the imaginary axis), or crossing (a quadruplet crossing the imaginary axis). We give a complete description of the behaviour of reversible periodic orbits in the vicinity of such a bifurcation point. For non-reversible periodic solutions. in the case of Hopf bifurcation with crossing eigenvalues. we obtain a generalization of the equivariant Hopf Theorem.

Resonance and chaos .1. First-order interior resonances

Analytical models for studying the dynamical behaviour of objects near interior, mean motion resonances are reviewed in the context of the planar, circular, restricted three-body problem. The predicted widths of the resonances are compared with the results of numerical integrations using Poincare surfaces of section with a mass ratio of 10(-3) (similar to the Jupiter-Sun case). It is shown that for very low eccentricities the phase space between the 2:1 and 3:2 resonances is predominantly regular, contrary to simple theoretical predictions based on overlapping resonance. A numerical study of the 'evolution' of the stable equilibrium point of the 3:2 resonance as a function of the Jacobi constant shows how apocentric libration at the 2:1 resonance arises; there is evidence of a similar mechanism being responsible for the centre of the 4:3 resonance evolving towards 3:2 apocentric libration. This effect is due to perturbations from other resonances and demonstrates that resonances cannot be considered in isolation. on theoretical grounds the maximum libration width of first-order resonances should increase as the orbit of the perturbing secondary is approached. However, in reality the width decreases due to the chaotic effect of nearby resonances.

Alternative paths to Earth-Moon transfer

The planar, circular, restricted three-body problem predicts the existence of periodic orbits around the Lagrangian equilibrium point L1. Considering the Earth-lunar-probe system, some of these orbits pass very close to the surfaces of the Earth and the Moon. These characteristics make it possible for these orbits, in spite of their instability, to be used in transfer maneuvers between Earth and lunar parking orbits. The main goal of this paper is to explore this scenario, adopting a more complex and realistic dynamical system, the four-body problem Sun-Earth-Moon-probe. We defined and investigated a set of paths, derived from the orbits around L1, which are capable of achieving transfer between low-altitude Earth (LEO) and lunar orbits, including high-inclination lunar orbits, at a low cost and with flight time between 13 and 15 days.

Stability analysis of the attitude of artificial satellites subject to gravity gradient torque

Using a canonical formulation, the stability of the rotational motion of artificial satellites is analyzed considering perturbations due to the gravity gradient torque. Here Andoyer's variables are used to describe the rotational motion. One of the approaches that allow the analysis of the stability of Hamiltonian systems needs the reduction of the Hamiltonian to a normal form. Firstly equilibrium points are found. Using generalized coordinates, the Hamiltonian is expanded in the neighborhood of the linearly stable equilibrium points. In a next step a canonical linear transformation is used to diagonalize the matrix associated to the linear part of the system. The quadratic part of the Hamiltonian is normalized. Based in a Lie-Hori algorithm a semi-analytic process for normalization is applied and the Hamiltonian is normalized up to the fourth order. Once the Hamiltonian is normalized up to order four, the analysis of stability of the equilibrium point is performed using the theorem of Kovalev and Savichenko. This semi-analytical approach was applied considering some data sets of hypothetical satellites. For the considered satellites it was observed few cases of stable motion. This work contributes for space missions where the maintenance of spacecraft attitude stability is required.

Strategies for plane change of Earth orbits using lunar gravity and derived trajectories of family G

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

Alternative Transfers to the NEOs 99942 Apophis, 1994 WR12, and 2007 UW1 via Derived Trajectories from Periodic Orbits of Family G

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

Resonance and chaos: I. First-order interior resonances

Analytical models for studying the dynamical behaviour of objects near interior, mean motion resonances are reviewed in the context of the planar, circular, restricted threebody problem. The predicted widths of the resonances are compared with the results of numerical integrations using Poincaré surfaces of section with a mass ratio of 10-3 (similar to the Jupiter-Sun case). It is shown that for very low eccentricities the phase space between the 2:1 and 3:2 resonances is predominantly regular, contrary to simple theoretical predictions based on overlapping resonance. A numerical study of the 'evolution' of the stable equilibrium point of the 3:2 resonance as a function of the Jacobi constant shows how apocentric libration at the 2:1 resonance arises; there is evidence of a similar mechanism being responsible for the centre of the 4:3 resonance evolving towards 3:2 apocentric libration. This effect is due to perturbations from other resonances and demonstrates that resonances cannot be considered in isolation. On theoretical grounds the maximum libration width of first-order resonances should increase as the orbit of the perturbing secondary is approached. However, in reality the width decreases due to the chaotic effect of nearby resonances.

A barrier method for constrained nonlinear optimization using a modified Hopfield network

The ability of neural networks to realize some complex nonlinear function makes them attractive for system identification. This paper describes a novel barrier method using artificial neural networks to solve robust parameter estimation problems for nonlinear model with unknown-but-bounded errors and uncertainties. This problem can be represented by a typical constrained optimization problem. More specifically, a modified Hopfield network is developed and its internal parameters are computed using the valid-subspace technique. These parameters guarantee the network convergence to the equilibrium points. A solution for the robust estimation problem with unknown-but-bounded error corresponds to an equilibrium point of the network. Simulation results are presented as an illustration of the proposed approach.

Reversible Hamiltonian Liapunov center theorem

We study the existence of periodic solutions in the neighbourhood of symmetric (partially) elliptic equilibria in purely reversible Hamiltonian vector fields. These are Hamiltonian vector fields with an involutory reversing symmetry R. We contrast the cases where R acts symplectically and anti-symplectically. In case R acts anti-symplectically, generically purely imaginary eigenvalues are isolated, and the equilibrium is contained in a local two-dimensional invariant manifold containing symmetric periodic solutions encircling the equilibrium point. In case R acts symplectically, generically purely imaginary eigenvalues are doubly degenerate, and the equilibrium is contained in two two-dimensional invariant manifolds containing nonsymmetric periodic solutions encircling the equilibrium point. In addition, there exists a three-dimensional invariant surface containing a two-parameter family of symmetric periodic solutions.