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.

Optimization of orthodontic treatment using the Centrex System to retract anterior teeth

INTRODUÇÃO: a Ortodontia passa, atualmente, por um momento de importantes inovações e grande efervescência criativa. Somente para citar algumas mudanças introduzidas ou aprimoradas nos últimos anos, nós podemos relembrar a popularização dos braquetes autoligáveis e o surgimento da ancoragem absoluta com a utilização de implantes ortodônticos. No final da década de 1990, a adoção dos mini-implantes como ancoragem permitiu uma mudança de paradigma que tem influenciado até mesmo a forma de pensar a mecânica ortodôntica. A imbricação das especialidades de Ortodontia e Implantodontia, cujo início se deu com os preparos ortodônticos para posterior inserção de implantes protéticos, floresceu com o uso de implantes palatinos e, posteriormente, com a introdução de mini-implantes. O aprimoramento da técnica de inserção de mini-implantes com a introdução de parafusos autoperfurantes tem permitido, inclusive, o requinte do ortodontista concentrar em suas mãos o planejamento e a colocação dessa preciosa peça de ancoragem. Levando em consideração a versatilidade de posicionamento desses pequenos parafusos, foi desenvolvido um conceito que possibilita a construção de linhas de ação de força que buscam otimizar o planejamento e a previsibilidade da movimentação ortodôntica. OBJETIVO: apresentar alguns resultados clínicos de tratamentos conduzidos com o uso de um sistema de tratamento ortodôntico, o Centrex System, que aproxima a linha de ação da força do centro de resistência das unidades a serem movimentadas. O caminho trilhado até o seu desenvolvimento, cuja teoria mecânica foi apresentada anteriormente nesse periódico, será detalhado para uma melhor compreensão de seu funcionamento.

Chaotic vibrations of a nonideal electro-mechanical system

Nonideal systems are those in which one takes account of the influence of the oscillatory system on the energy supply with a limited power (Kononenko, 1969). In this paper, a particular nonideal system is investigated, consisting of a pendulum whose support point is vibrated along a horizontal guide by a two bar linkage driven by a DC motor, considered to be a limited power supply. Under these conditions, the oscillations of the pendulum are analyzed through the variation of a control parameter. The voltage supply of the motor is considered to be a reliable control parameter. Each simulation starts from zero speed and reaches a steady-state condition when the motor oscillates around a medium speed. Near the fundamental resonance region, the system presents some interesting nonlinear phenomena, including multi-periodic, quasiperiodic, and chaotic motion. The loss of stability of the system occurs through a saddle-node bifurcation, where there is a collision of a stable orbit with an unstable one, which is approximately located close to the value of the pendulum's angular displacement given by alpha (C)= pi /2. The aims of this study are to better understand nonideal systems using numerical simulation, to identify the bifurcations that occur in the system, and to report the existence of a chaotic attractor near the fundamental resonance. (C) 2001 Elsevier B.V. Ltd. All rights reserved.

On an optimal control design for Rossler system

In this Letter, an optimal control strategy that directs the chaotic motion of the Rossler system to any desired fixed point is proposed. The chaos control problem is then formulated as being an infinite horizon optimal control nonlinear problem that was reduced to a solution of the associated Hamilton-Jacobi-Bellman equation. We obtained its solution among the correspondent Lyapunov functions of the considered dynamical system. (C) 2004 Elsevier B.V All rights reserved.

NONLINEAR DIFFUSION PROCESS IN A BENARD SYSTEM AT THE CRITICAL-POINT FOR THE ONSET OF CONVECTION

The evolution equation governing surface perturbations of a shallow fluid heated from below at the critical Rayleigh number for the onset of convective motion, and with boundary conditions leading to zero critical wave number, is obtained. A solution for negative or cooling perturbations is explicitly exhibited, which shows that the system presents sharp propagating fronts.

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.

Postural control as a function of self- and object-motion perception

The goals of this study were to examine the visual information influence on body sway as a function of self- and object-motion perception and visual information quality. Participants that were aware (object-motion) and unaware (self-motion) of the movement of a moving room were asked to stand upright at five different distances from its frontal wall. The visual information effect on body sway decreased when participants were aware about the sensory manipulation. Moreover, while the visual influence on body sway decreased as the distance increased in the self-motion perception, no effects were observed in the object-motion mode. The overall results indicate that postural control system functioning can be altered by prior knowledge, and adaptation due to changes in sensory quality seem to occur in the self- but not in the object-motion perception mode. (C) 2004 Elsevier B.V.. All rights reserved.

Using transient and steady state considerations to investigate the mechanism of loss of stability of a dynamical system

This work presents the complete set of features for solutions of a particular non-ideal mechanical system near the fundamental and near to a secondary resonance region. The system comprises a pendulum with a horizontally moving suspension point. Its motion is the result of a non-ideal rotating power source (limited power supply), acting oil the Suspension point through a crank mechanism. Main emphasis is given to the loss of stability, which occurs by a sequence of events, including intermittence and crisis, when the system reaches a chaotic attractor. The system also undergoes a boundary-crisis, which presents a different aspect in the bifurcation diagram due to the non-ideal supposition. (c) 2004 Published by Elsevier B.V.

Synthesis Pengo System plates for the treatment of long-bone diaphyseal fractures in dogs

A Brazilian orthopaedic company designed a stainless steel plate called Synthesis Pengo System (S.P.S.), which has one fixed and one changeable extremity. According to the assembly of the changeable extremity, it is possible to obtain dynamization or neutralization of the fracture site. Since the S.P.S. plate was developed for use in human patients, the aim of this study was to evaluate this system in long-bone diaphyseal fractures in dogs. Eight dogs with closed diaphyseal fractures of the femur (n = 1), radius and ulna (n = 5), and tibia (n = 2) were used. Patients were aged seven months to three years and weighed 18 to 31.2 kg. The S.P.S. plate was assembled with one fixed extremity and one changeable extremity in dynamization mode. The trail bar was positioned for synthesis modules with holes for cortical screws. The modules were positioned close to one another in two fractures and for away from the fracture site in the others. The bone healing occurred by external callus. Since motion at the fracture site determines the amount of callus required, the secondary bone healing that was observed in all of the cases indicated less rigid fixation of this system. A potential benefit of this system was a lesser interface contact with the bone since it was only done by trail bar. The major disadvantage was the prominence of the implant. It was possible to conclude that the S.P.S. plate appears to be a suitable method for the treatment of diaphyseal fractures in dogs.

Stability regions around the components of the triple system 2001 SN263

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Escape in a nonideal electro-mechanical system

In this work a particular system is investigated consisting of a pendalum whose point of support is vibrated along a horizontal guide by a two bar linkage driven from a DC motor, considered as a limited power source. This system is nonideal since the oscillatory motion of the pendulum influences the speed of the motor and vice-versa, reflecting in a more complicated dynamical process. This work comprises the investigation of the phenomena that appear when the frequency of the pendulum draws near a secondary resonance region, due to the existing nonlinear interactions in the system. Also in this domain due to the power limitation of the motor, the frequency of the pendulum can be captured at resonance modifying completely the final response of the system. This behavior is known as Sommerfield effect and it will be studied here for a nonlinear system.

An overview on a nonideal system with three and a half degrees of freedom

The present paper studies a system comprised of two blocks connected by springs and dampers, and a DC motor with limited power supply fixed on a block, characterizing a non-ideal problem. This DC motor exciting the system causes interactions between the motor and the structure supporting it. Because of that, the non-ideal mathematical formulation of the problem has one and a half extra degree of freedom than the ideal one. A suitable choice of physical parameters leads to internal resonance conditions, that is, its natural frequencies are multiple of each other, by a known integer quantity. The purpose here is to study the dynamic behavior of the system using an analytical method based on perturbation techniques. The literature shows that the averaging method is the more flexible method concerning non-ideal problems. Summarizing, an steady state solution in amplitude and phase coordinates was obtained with averaging method showing the dependence of the structure amplitudes with the rotation frequency of the motor. Moreover, this solution shows that on of the amplitude coordinates has influence in the determination of the stationary rotation frequency. The analytical solution obtained shows the presence of the rotation frequency in expressions representing the oscillations of the structure, and the presence of amplitude coordinates in expressions describing the dynamic motion of the DC motor. These characteristics show the influence not only of the motor on structure but also of the response of the structure on dynamical behavior of the motor. Copyright © 2005 by ASME.

Dynamic analysis of a new piezoelectric flextensional actuator using the J1-J4 optical interferometric method

Piezoelectric actuators are widely used in positioning systems which demand high resolution such as scanning microscopy, fast mirror scanners, vibration cancellation, cell manipulation, etc. In this work a piezoelectric flextensional actuator (PFA), designed with the topology optimization method, is experimentally characterized by the measurement of its nanometric displacements using a Michelson interferometer. Because this detection process is non-linear, adequate techniques must be applied to obtain a linear relationship between an output electrical signal and the induced optical phase shift. Ideally, the bias phase shift in the interferometer should remain constant, but in practice it suffers from fading. The J1-J4 spectral analysis method provides a linear and direct measurement of dynamic phase shift in a no-feedback and no-phase bias optical homodyne interferometer. PFA application such as micromanipulation in biotechnology demands fast and precise movements. So, in order to operate with arbitrary control signals the PFA must have frequency bandwidth of several kHz. However as the natural frequencies of the PFA are low, unwanted dynamics of the structure are often a problem, especially for scanning motion, but also if trajectories have to be followed with high velocities, because of the tracking error phenomenon. So the PFA must be designed in such a manner that the first mechanical resonance occurs far beyond this band. Thus it is important to know all the PFA resonance frequencies. In this work the linearity and frequency response of the PFA are evaluated up to 50 kHz using optical interferometry and the J1-J4 method.

Electromyographyc evaluation of movements of lower limb in double pulley system equipment: Comparison between gastrocnemius (caput laterale) and gluteus maximus

It was evaluated movements of lower limb in the double pulley system equipment on ten male volunteers during contraction of gastrocnemius (caput laterale ) and gluteus maximus muscles in the following movements: 1) hip extension with extended knee and erect trunk, 2) hip extension with flexed knee and erect trunk, 3) hip extension with flexed knee and erect trunk, 3) hip extension with extended knee and inclined trunk, 5) hip abduction along the midline, 7) hip abduction with extension beyond the midline, 8) adduction with hip flexion beyond the midline, 8) adduction with hip flexion beyond the midline, and 9) adduction with hip extension beyond the midline. Myoelectric signals were taken up by Lec Tec surface electrodes connected to a 6-channel Lynx electromyographic signal amplifier coupled with a computer equipped with a model CAD 10/26 analogue digital conversion board and with a specific software for signal recording and analysis. We observed weak gastrocnemius muscle activity for all movements studied. In the case of gluteus maximus, the most important potentials were observed for movement 2, while for the remaining movements the actions were of reasonable intensity. Compared to gluteus, gastrocnemius was less required for all movements.