Time-dependent properties in two-dimensional and Hamiltonian mappings

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

THREE TIME SCALE SINGULAR PERTURBATION PROBLEMS AND NONSMOOTH DYNAMICAL SYSTEMS

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

Efeitos de campos elétrico e magnético em um sistema dissipativo pulsante

The main idea of this work is to understand and analyze the dynamical aspects of the motion of a particle moving in the annular billiard, which corresponds to two circles of radius R and r (rorbits and do not contribute to the Fermi acceleration indeed. However, in presence of the electric field, to same values, the magnetic one together can improve this referred process, obtaining greater energy values to the same number of iterations. These results are applied to the concentric case, that was reported did not haven any significant energy gain on the free particle motion

Dinâmica de rotação de exoplanetas tipo terrestre com perturbação de terceiro corpo

In this work we study some topics of Celestial Mechanics, namely the problem of rigid body rotation and “spin-orbit” resonances. Emphasis is placed on the problem formulation and applications to some exoplanets with physical parameters (e.g. mass and radius) compatible with a terrestrial type constitution (e.g. rock) belonging to multiple planetary systems. The approach is both analytical and numerical. The analytical part consists of: i) the deduction of the equation of motion for the rotation problem of a spherical body with no symmetry, disturbed by a central body; ii) modeling the same problem by including a third-body in the planet-star system; iii) formulation of the concept of “spin-orbit” resonance in which the orbital period of the planet is an integer multiple of the rotation’s period. Topics of dynamical systems (e.g. equilibrium points, chaos, surface sections, etc.) will be included at this stage. In the numerical part simulations are performed with numerical models developed in the previous analytical section. As a first step we consider the orbit of the planet not perturbed by a third-body in the star-planet system. In this case the eccentricity and orbital semi-major axis of the planet are constants. Here the technique of surface sections, widely used in dynamical systems are applied. Next, we consider the action of a third body, developing a more realistic model for planetary rotation. The results in both cases are compared. Since the technique of disturbed surface sections is no longer applicable, we quantitatively evaluate the evolution of the characteristic angles of rotation (e.g. physical libration) by studying the evolution of individual orbits in the dynamically important regions of phase space, the latter obtained in the undisturbed case

Reanálise das defasagens de Prometeu e Pandora

In the present work it is proposed to do a revision on some studies on the dynamics of the Prometheus-Pandora system. In special, those studies that deal with anomalous behaviours observed on its components, identi ed as angular lags in these satellite`s orbits. Initially, it is presented a general description, contextualising the main characteristics of this system. The main publications related to this subject are analised and commented, in chronological order, showing the advances made in the knowledge of such dynamics. An analysis of the initial conditions, used by Goldreich e Rappaport (2003a ,b) e Cruz (2004), obtained through observations made by the Voyager 1 and 2 spacecrafts and by the Hubble space telescope, it is made in order to try to reproduce their results. However, no clear conclusion of the values used were found. The tests addopted in the analysis are from Cruz (2004), which reproduced the results and o ered a new explanation on the origin of the observed angular lags. The addopetd methodology involves the numerical integration of the equations of motion of the system, including the zonal harmonics J2, J4 and J6 of Saturn's gravitational potential. A fundamental consideration in this study is the use of geometric elements instead of osculating elements. It was found the set of initial data that best reproduces the results from Goldreich e Rappaport (2003a, b) and Cruz (2004)

Controllability of control systems on complex simple lie groups and the topology of flag manifolds

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

Study of some strategies for disposal of the gnss satellites

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dynamics of classical particles in oval or elliptic billiards with a dispersing mechanism

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

A dissipative Fermi-Ulam model under two different kinds of dissipation

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

Resonance capture at arbitrary inclination

Resonance capture is studied numerically in the three-body problem for arbitrary inclinations. Massless particles are set to drift from outside the 1: 5 resonance with a Jupiter-mass planet thereby encountering the web of the planet's diverse mean motion resonances. Randomly constructed samples explore parameter space for inclinations from 0 to 180 degrees with 5 degrees increments totalling nearly 6 x 10(5) numerical simulations. 30 resonances internal and external to the planet's location are monitored. We find that retrograde resonances are unexpectedly more efficient at capture than prograde resonances and that resonance order is not necessarily a good indicator of capture efficiency at arbitrary inclination. Capture probability drops significantly at moderate sample eccentricity for initial inclinations in the range [10 degrees,110 degrees]. Orbit inversion is possible for initially circular orbits with inclinations in the range [60 degrees,130 degrees]. Capture in the 1:1 co-orbital resonance occurs with great likelihood at large retrograde inclinations. The planet's orbital eccentricity, if larger than 0.1, reduces the capture probabilities through the action of the eccentric Kozai-Lidov mechanism. A capture asymmetry appears between inner and outer resonances as prograde orbits are preferentially trapped in inner resonances. The relative capture efficiency of retrograde resonance suggests that the dynamical lifetimes of Damocloids and Centaurs on retrograde orbits must be significantly larger than those on prograde orbits implying that the recently identified asteroids in retrograde resonance, 2006 BZ8, 2008 SO218, 2009 QY6 and 1999 LE31 may be among the oldest small bodies that wander between the outer giant planets.

Strain rates estimated by geodetic observations in the Borborema Province, Brazil

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The evolution of a Pluto-like system during the migration of the ice giants

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

Planet formation in a triple stellar system: implications of the third star's orbital inclination

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

Chaotic Dynamics in a Low-Energy Transfer Strategy to the Equilateral Equilibrium Points in the Earth-Moon System

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

Dinâmica secular rotacional de corpos tri-axiais: expansão de V em ressonâncias de primeira ordem

Consider a finite body of mass m (C1) with moments of inertia A, B and C. This body orbits another one of mass much larger M (C2), which at first will be taken as a point, even if it is not completely spherical. The body C1, when orbit C2, performs a translational motion near a Keplerian. It will not be a Keplerian due to external disturbances. We will use two axes systems: fixed in the center of mass of C1 and other inertial. The C1 attitude, that is, the dynamic rotation of this body is know if we know how to situate mobile system according to inertial axes system. The strong influence exerted by C2 on C1, which is a flattened body, generates torques on C1, what affects its dynamics of rotation. We will obtain the mathematical formulation of this problem assuming C1 as a planet and C2 as the sun. Also applies to case of satellite and planet. In the case of Mercury-Sun system, the disturbing potential that governs rotation dynamics, for theoretical studies, necessarily have to be developed by powers of the eccentricity. As is known, such expansions are delicate because of the convergence issue. Thus, we intend to make a development until the third order (superior orders are not always achievable because of the volume of terms generated in cases of first-order resonances). By defining a modern set of canonical variables (Andoyer), we will assemble a disturbed Hamiltonian problem. The Andoyer's Variables allow to define averages, which enable us to discard short-term effects. Our results for the resonant angle variation of Mercury are in full agreement with those obtained by D'Hoedt & Lemaître (2004) and Rambaux & Bois (2004)