Dynamics of some fictitious satellites of Venus and Mars

The dynamics of some fictitious satellites of Venus and Mars are studied considering only solar perturbation and the oblateness of the planet, as disturbing forces. Several numerical integrations of the averaged system, taking different values of the obliquity of ecliptic (a), show the existence of strong chaotic motion, provided that the semi major axis is near a critical value. As a consequence, large increase of eccentricities occur and the satellites may collide with the planet or cross possible internal orbits. Even starting from almost circular and equatorial orbits, most satellites can easily reach prohibitive values. The extension of the chaotic zone depends clearly on the value ε, so that, previous regular regions may become chaotic, provided ε increases sufficiently. © 1999 Elsevier Science Ltd. All rights reserved.

Dynamics of a piecewise-linear oscillator with limited power supply

We discuss dynamics of a vibro-impact system consisting of a cart with an piecewise-linear restoring force, which vibrates under driving by a source with limited power supply. From the point of view of dynamical systems, vibro-impact systems exhibit a rich variety of phenomena, particularly chaotic motion. In our analyzes, we use bifurcation diagrams, basins of attractions, identifying several non-linear phenomena, such as chaotic regimes, crises, intermittent mechanisms, and coexistence of attractors with complex basins of attraction. © 2009 by ASME.

On a control design to an AFM microcantilever beam, operating in a tapping-mode, with irregular behavior

In last decades, control of nonlinear dynamic systems became an important and interesting problem studied by many authors, what results the appearance of lots of works about this subject in the scientific literature. In this paper, an Atomic Force Microscope micro cantilever operating in tapping mode was modeled, and its behavior was studied using bifurcation diagrams, phase portraits, time history, Poincare maps and Lyapunov exponents. Chaos was detected in an interval of time; those phenomena undermine the achievement of accurate images by the sample surface. In the mathematical model, periodic and chaotic motion was obtained by changing parameters. To control the chaotic behavior of the system were implemented two control techniques. The SDRE control (State Dependent Riccati Equation) and Time-delayed feedback control. Simulation results show the feasibility of the bothmethods, for chaos control of an AFM system. Copyright © 2011 by ASME.

Nonlinear control system applied to atomic force microscope including parametric errors

The performance of the optimal linear feedback control and of the state-dependent Riccati equation control techniques applied to control and to suppress the chaotic motion in the atomic force microscope are analyzed. In addition, the sensitivity of each control technique regarding to parametric uncertainties are considered. Simulation results show the advantages and disadvantages of each technique. © 2013 Brazilian Society for Automatics - SBA.

Dinâmica de uma partícula coorbital a um sistema de satélites

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

Uso de absorvedores de vibrações eletromecânicos lineares e não-lineares em sistemas não-lineares e não-ideais

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Dinâmica não linear, caos, e controle na microscopia de força atômica

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Caos e controle de microviga em balanço de um microscópio de força atômica, operando em modo intermitente, na ressonância

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Movimento orbital de satélites artificiais: efeitos ressonantes

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

Application of passive control to energy harvester efficiency using a nonideal portal frame structural support system

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

Análise dinâmica de mecanismo articulado de suspensão com não-linearidade na rigidez devido à geometria e à excitação por desbalanceamento rotativo na condição não ideal

Pós-graduação em Engenharia Mecânica - FEB

On nonlinear dynamics and control of a robotic arm with chaos

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Application of Wisdom's perturbative method for 5 : 2 and 7 : 3 resonances

Wisdom's method is applied to 5 : 2 and 7 : 3 resonances. Comparisons with Yoshikawa's nontruncated model are performed: for moderate values of eccentricity, agreement is good, especially for the 5 : 2 resonance. A clear difference between the 5 : 2 and the 7 : 3 resonances is observed: the former (like the 3 : 1 resonance) can suffer significant variations of eccentricity, even starting from very small values close to 0, while the latter seems to undergo such variations but the minimum eccentricity cannot be less than a value near 0.1. In the 7 : 3 resonance, some chaotic motion trapped in a region of very small eccentricity is possible. This is in contrast with the 5 : 2 commensurability, since chaos in this case seems to be always related to significant variations of eccentricity. Recent calculations performed by Šidlichovskÿ using mapping techniques show agreement with the results presented here. © 1992.

Chaos control and sensitivity analysis of a double pendulum arm excited by an RLC circuit based nonlinear shaker

In this paper the dynamical interactions of a double pendulum arm and an electromechanical shaker is investigated. The double pendulum is a three degree of freedom system coupled to an RLC circuit based nonlinear shaker through a magnetic field, and the capacitor voltage is a nonlinear function of the instantaneous electric charge. Numerical simulations show the existence of chaotic behavior for some regions in the parameter space and this behaviour is characterized by power spectral density and Lyapunov exponents. The bifurcation diagram is constructed to explore the qualitative behaviour of the system. This kind of electromechanical system is frequently found in robotic systems, and in order to suppress the chaotic motion, the State-Dependent Riccati Equation (SDRE) control and the Nonlinear Saturation control (NSC) techniques are analyzed. The robustness of these two controllers is tested by a sensitivity analysis to parametric uncertainties.

Dinâmica não linear e controle de um sistema vibratório modelado com memória de forma e, excitado por fontes de energia do tipo ideal e não ideal

Pós-graduação em Engenharia Mecânica - FEB