On the dynamics of some resonances of Phobos in the future

A probable capture of Phobos into an interesting resonance was presented in our previous work. With a simple model, considering Mars in a Keplerian and circular orbit, it was shown that once captured in the resonance, the inclination of the satellite reaches very high values. Here, the integrations are extended to much longer times and escape situations are analyzed. These escapes are due to the interaction of new additional resonances, which appear as the inclination starts to increase reaching some specific values. Compared to classical capture in mean motion resonances, we see some interesting differences in this problem. We also include the effect of Mars' eccentricity in the process of the capture. The role played by this eccentricity becomes important, particularly when Phobos encounters a double resonance at a approximate to 2.619R(M). Planetary perturbations acting on Mars and variation of its equator are also included. In general, some possible scenarios of the future of Phobos are presented.

Some aspects of the dynamics of fictitious Earth's satellites

In this work we study the dynamics of fictitious satellites of the Earth. In the first part we do not consider the effect of the Moon and study the dynamics in the restrict three-body model, i.e., a massless satellite under the effect of the gravitational force of an oblate Earth and that of the Sun. We show that a satellite starting with an almost circular orbit suffers very large variations of eccentricity, depending on the initial inclination of the orbit with respect to the reference plane. As the eccentricity may be driven to very large values (approximate to0.9) mutual collisions between satellites or collisions with the planet may occur. In the second part, we include the gravitational effect of the Moon. In this case, we find two regions with large variations of eccentricity due to the presence of the Moon. Consequently, in both scenarios, we find some large regions of the phase space where the long-term stability of some fictitious Earth's satellites is not possible. (C) 2001 Elsevier B.V. Ltd. All rights reserved.

Analytical study of the nonlinear behavior of a shape memory oscillator: Part II-resonance secondary

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Remarks on an Optimal Linear Control Design Applied to a Nonideal and an Ideal Structure Coupled to an Essentially Nonlinear Oscillator

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

Scaling dynamics for a particle in a time-dependent potential well

Some dynamical properties for a classical particle confined in an infinitely deep box of potential containing a periodically oscillating square well are studied. The dynamics of the system is described by using a two-dimensional non-linear area-preserving map for the variables energy and time. The phase space is mixed and the chaotic sea is described using scaling arguments. Scaling exponents are obtained as a function of all the control parameters, extending the previous results obtained in the literature. (c) 2012 Elsevier B.V. All rights reserved.

On energy pumping, synchronization and beat phenomenon in a nonideal structure coupled to an essentially nonlinear oscillator

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

Dynamics of Enceladus and Dione inside the 2:1 mean-motion resonance under tidal dissipation

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

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.

Suppressing Fermi acceleration in two-dimensional driven billiards

We consider a dissipative oval-like shaped billiard with a periodically moving boundary. The dissipation considered is proportional to a power of the velocity V of the particle. The three specific types of power laws used are: (i) F proportional to-V; (ii) F proportional to-V-2 and (iii) F proportional to-V-delta with 1 < delta < 2. In the course of the dynamics of the particle, if a large initial velocity is considered, case (i) shows that the decay of the particle's velocity is a linear function of the number of collisions with the boundary. For case (ii), an exponential decay is observed, and for 1 < delta < 2, an powerlike decay is observed. Scaling laws were used to characterize a phase transition from limited to unlimited energy gain for cases (ii) and (iii). The critical exponents obtained for the phase transition in the case (ii) are the same as those obtained for the dissipative bouncer model. Therefore near this phase transition, these two rather different models belong to the same class of universality. For all types of dissipation, the results obtained allow us to conclude that suppression of the unlimited energy growth is indeed observed.

Decay of energy and suppression of Fermi acceleration in a dissipative driven stadium-like billiard

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

Scaling investigation for the dynamics of charged particles in an electric field accelerator

Some dynamical properties of an ensemble of trajectories of individual (non-interacting) classical particles of mass m and charge q interacting with a time-dependent electric field and suffering the action of a constant magnetic field are studied. Depending on both the amplitude of oscillation of the electric field and the intensity of the magnetic field, the phase space of the model can either exhibit: (i) regular behavior or (ii) a mixed structure, with periodic islands of regular motion, chaotic seas characterized by positive Lyapunov exponents, and invariant Kolmogorov-Arnold-Moser curves preventing the particle to reach unbounded energy. We define an escape window in the chaotic sea and study the transport properties for chaotic orbits along the phase space by the use of scaling formalism. Our results show that the escape distribution and the survival probability obey homogeneous functions characterized by critical exponents and present universal behavior under appropriate scaling transformations. We show the survival probability decays exponentially for small iterations changing to a slower power law decay for large time, therefore, characterizing clearly the effects of stickiness of the islands and invariant tori. For the range of parameters used, our results show that the crossover from fast to slow decay obeys a power law and the behavior of survival orbits is scaling invariant. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4772997]

Lacustrine records of Holocene flood pulse dynamics in the Upper Paraguay River watershed (Pantanal wetlands, Brazil)

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

Surface effects on vortex dynamics in thin type-II superconducting stripes with random pinning

We analyze the dynamics of a driven vortex lattice moving in a thin Superconducting stripe. The two dimensional stripe is assumed to be finite in the longitudinal direction, where we take into account the Surface effects, and infinite in the transversal direction. The numerical simulations are performed using the Langevin dynamics, including the vortex-vortex interaction, interaction of vortices with the surface current, vortex images, transport current and randomly distributed pinning centers. We show results for the differential resistivity and the vortex trajectories as a function of the external force. (C) 2004 Elsevier B.V. All rights reserved.

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.

Criteria for mixed grids in computational fluid dynamics

The finite volume method is used as a numerical method for solving the fluid flow equations. This method is appropriate to employ under structured and unstructured meshes. Mixed grids, combining both types of grids, are investigated. The coupling of different grids is done by overlapping strategy. The computational effort for the mixed grid is evaluated by the CPU-time, with different percentage of covering area of the unstructured mesh. The present scheme is tested for the driven cavity problem, where the incompressible fluid is integrated by calculating the velocity fields and computing the pressure field in each time step. Several schemes for unstructured grid are examined, and the compatibility condition is applied to check their consistency. A scheme to verify the compatibility condition for the unstructured grids is presented. (c) 2006 IMACS. Published by Elsevier B.V. All rights reserved.