Dynamics of a spacecraft and normalization around Lagrangian points in the Neptune-Triton system

The problem of a spacecraft orbiting the Neptune-Triton system is presented. The new ingredients in this restricted three body problem are the Neptune oblateness and the high inclined and retrograde motion of Triton. First we present some interesting simulations showing the role played by the oblateness on a Neptune's satellite, disturbed by Triton. We also give an extensive numerical exploration in the case when the spacecraft orbits Triton, considering Sun, Neptune and its planetary oblateness as disturbers. In the plane a x I (a = semi-major axis, I = inclination), we give a plot of the stable regions where the massless body can survive for thousand of years. Retrograde and direct orbits were considered and as usual, the region of stability is much more significant for the case of direct orbit of the spacecraft (Triton's orbit is retrograde). Next we explore the dynamics in a vicinity of the Lagrangian points. The Birkhoff normalization is constructed around L-2, followed by its reduction to the center manifold. In this reduced dynamics, a convenient Poincare section shows the interplay of the Lyapunov and halo periodic orbits, Lissajous and quasi-halo tori as well as the stable and unstable manifolds of the planar Lyapunov orbit. To show the effect of the oblateness, the planar Lyapunov family emanating from the Lagrangian points and three-dimensional halo orbits are obtained by the numerical continuation method. Published by Elsevier Ltd. on behalf of COSPAR.

Centers on center manifolds in the Lu system

We confirm a conjecture of Mello and Coelho [Phys. Lett. A 373 (2009) 1116] concerning the existence of centers on local center manifolds at equilibria of the Lu system of differential equations on R(3). Our proof shows that the local center manifolds are algebraic ruled surfaces, and are unique. (C) 2011 Elsevier B.V. All rights reserved.

On the dynamics of free and excited oscillations of a simple portal frame foundation

In this paper we search for the dynamics of a simple portal structure in the free and in the periodic excitation cases. By using the Center Manifold approach and Averaging Method, we obtain results on both stability and bifurcation of equilibrium points and periodic orbits. (C) 2005 Elsevier Ltd. All rights reserved.

On the appearance of a Hopf bifurcation in a non-ideal mechanical problem

In this paper we studied a non-ideal system with two degrees of freedom consisting of a dumped nonlinear oscillator coupled to a rotatory part. We investigated the stability of the equilibrium point of the system and we obtain, in the critical case, sufficient conditions in order to obtain an appropriate Normal Form. From this, we get conditions for the appearance of Hopf Bifurcation when the difference between the driving torque and the resisting torque is small. It was necessary to use the Bezout Theorem, a classical result of Algebraic Geometry, in the obtaining of the foregoing results. (C) 2003 Elsevier Ltd. All rights reserved.

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.

Regularization of discontinuous vector fields on R-3 via singular perturbation

Singular perturbations problems in dimension three which are approximations of discontinuous vector fields are studied in this paper. The main result states that the regularization process developed by Sotomayor and Teixeira produces a singular problem for which the discontinuous set is a center manifold. Moreover, the definition of' sliding vector field coincides with the reduced problem of the corresponding singular problem for a class of vector fields.

Uma análise da dinâmica do pêndulo eletromecânico utilizando a teoria de pertubações

Pós-graduação em Matemática - IBILCE

Variedade central para laços homoclínicos

Pós-graduação em Matemática - IBILCE

Kinetics and mechanism of the induced redox reaction of [Ni(cyclam)](2+) promoted by SO5 center dot-

Oxidation of [Ni(cyclam)](2+), cyclam = 1,4,8,11-tetraazacyclotetradecane, accelerated by sulfur dioxide, was studied spectrophotometrically by following the formation of [Ni(cyclam)](3+) under the conditions: [Ni(cyclam)](2+) = 6.0 x 10(-3) M; initial [Ni(cyclam)](3+) = 8.0 x 10(-6) M; [cyclam] = 6.0 x 10(-3) M; [SO2] = (1.0-5.0) x 10(-4) M and 1.0 M perchloric acid in oxygen saturated solutions at 25.0 degrees C and ionic strength = 1.0 M. The oxidation reaction exhibits autocatalytic behavior in which the induction period depends on the initial Ni(III) concentration. A kinetic study of the reduction of Ni(III) by SO2 under anaerobic conditions, and the oxidation of Ni(II), showed that the rate-determining step involves reduction of Ni(III) by SO2 to produce the SO3.- radical, which rapidly reacts with dissolved oxygen to produce SO5.- and rapidly oxidizes Ni(II). The results clearly show a redox cycling process which depends on the balance of SO2 and oxygen concentrations in solution.

Multidisciplinary approach to chronic pain from myofascial pain dysfunction syndrome: A four-year experience at a Brazilian center

Chronic pain is the major complaint of myofascial pain dysfunction syndrome (MPDS) and is a complex problem which involves physical, psychological and social aspects, the etiology of MPDS is multifactorial and the multidisciplinary approach is essential for differential diagnosis and for comprehensive treatment planning, In 1993, the Dental School of Piracicaba-UNICAMP, Brazil, opened a Center for Pain Studies (CPS), staffed by health care providers including, dentists, psychologists, physicians, physiotherapists and phonoaudiologists. The major aims of the CPS are to provide clinical care and to develop basic and applied research, Sixty-two MPDS patients had been admitted to the CPS by 1997, There were 60 females and 2 males, mean age -32.5 years, the mean duration of chronic pain was 48 months. Pain intensity and unpleasantness were measured employing the Visual Analogue Scale, the tendency to develop stress-related diseases was assessed by the Social Readjustment de Scale, There was a mean reduction of chronic pain of 69.89% and 71.78% relative to intensity and unpleasantness, respectively, the experience of clinical attendance at a multidisciplinary center showed the relevance of a team consisting of health care providers from different specialties with well-established aims, completely integrated and sensitive enough to understand the painful complaints of MPDS patients.

Kinetic aspects of ion exchange in KhFek[Fe(CN)(6)](l)center dot mH(2)O compounds: A combined electrical and mass transfer functions approach

The present paper quantifies and develops the kinetic aspects involved in the mechanism of interplay between electron and ions presented elsewhere(1) for KhFek[Fe(CN)(6)](l)center dot mH(2)O (Prussian Blue) host materials. Accordingly, there are three different electrochemical processes involved in the PB host materials: H3O+, K+, and H+ insertion/extraction mechanisms which here were fully kinetically studied by means of the use of combined electronic and mass transfer functions as a tool to separate all the processes. The use of combined electronic and mass transfer functions was very important to validate and confirm the proposed mechanism. This mechanism allows the electrochemical and chemical processes involved in the KhFek[Fe(CN)(6)](l)center dot mH(2)O host and Prussian Blue derivatives to be understood. In addition, a formalism was also developed to consider superficial oxygen reduction. From the analysis of the kinetic processes involved in the model, it was possible to demonstrate that the processes associated with K+ and H+ exchanges are reversible whereas the H3O+ insertion process was shown not to present a reversible pattern. This irreversible pattern is very peculiar and was shown to be related to the catalytic proton reduction reaction. Furthermore, from the model, it was possible to calculate the number density of available sites for each intercalation/deintercalation processes and infer that they are very similar for K+ and H+. Hence, the high prominence of the K+ exchange observed in the voltammetric responses has a kinetic origin and is not related to the amount of sites available for intercalation/deintercalation of the ions.

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.

Optimal moment to change pressure regulator and sprayer kit on center pivot irrigation machines: application to a study case

A theoretical model developed by the authors for determining the optimal moment to substitute sprayer and pressure regulator kit on a center pivot irrigating potatoes and beans has been applied. The methodology compares the sum of the costs due to additional consumption of water and energy, maintenance and labor, as well as yield losses associated to areas with deficit or over irrigation to the costs due to buy and install a new sprinkling set on the pivot. The results showed that for a reduction of 3.07% of the Hermann and Hein’s Uniformity Coefficient (UCh), the substitution of the sprinkling module on the pivot is justified when potatoes and beans are cultivated.

Photoelectrochemical reduction of CO2 on Cu/Cu2O films: Product distribution and pH effects

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