Peculiar trajectories around the Lagrangian equilateral points

In the present work we analyse the behaviour of a particle under the gravitational influence of two massive bodies and a particular dissipative force. The circular restricted three body problem, which describes the motion of this particle, has five equilibrium points in the frame which rotates with the same angular velocity as the massive bodies: two equilateral stable points (L-4, L-5) and three colinear unstable points (L-1, L-2, L-3). A particular solution for this problem is a stable orbital libration, called a tadpole orbit, around the equilateral points. The inclusion of a particular dissipative force can alter this configuration. We investigated the orbital behaviour of a particle initially located near L4 or L5 under the perturbation of a satellite and the Poynting-Robertson drag. This is an example of breakdown of quasi-periodic motion about an elliptic point of an area-preserving map under the action of dissipation. Our results show that the effect of this dissipative force is more pronounced when the mass of the satellite and/or the size of the particle decrease, leading to chaotic, although confined, orbits. From the maximum Lyapunov Characteristic Exponent a final value of gamma was computed after a time span of 10(6) orbital periods of the satellite. This result enables us to obtain a critical value of log y beyond which the orbit of the particle will be unstable, leaving the tadpole behaviour. For particles initially located near L4, the critical value of log gamma is -4.07 and for those particles located near L-5 the critical value of log gamma is -3.96. (c) 2006 Elsevier B.V. All rights reserved.

Classical and quantal aspects of resonant normal forms

The Birkhoff-Gustavson normal form is employed to study separately chaos and resonances in a system with two degrees of freedom. In the integrable regime, tunnelling effects are appreciable when the nearest level spacings show oscillations. Tunnelling among states in the libration and rotation tori regions is also observed. The regularity of avoided crossings due to tunnelling indicates a collective effect and is associated with an isolated resonance. The spectral fluctuations also show a strong level correlation. The Husimi distribution, on the other hand, is insensitive to avoided crossings. An integrable approximation to the overlap of resonances is obtained and a theoretical description is given for an isolated cubic resonance plus a complex orbit. In the non-integrable regime chaos is stronger after overlapping and preferentially at low energies.

Resonance and chaos: I. First-order interior resonances

Analytical models for studying the dynamical behaviour of objects near interior, mean motion resonances are reviewed in the context of the planar, circular, restricted threebody problem. The predicted widths of the resonances are compared with the results of numerical integrations using Poincaré surfaces of section with a mass ratio of 10-3 (similar to the Jupiter-Sun case). It is shown that for very low eccentricities the phase space between the 2:1 and 3:2 resonances is predominantly regular, contrary to simple theoretical predictions based on overlapping resonance. A numerical study of the 'evolution' of the stable equilibrium point of the 3:2 resonance as a function of the Jacobi constant shows how apocentric libration at the 2:1 resonance arises; there is evidence of a similar mechanism being responsible for the centre of the 4:3 resonance evolving towards 3:2 apocentric libration. This effect is due to perturbations from other resonances and demonstrates that resonances cannot be considered in isolation. On theoretical grounds the maximum libration width of first-order resonances should increase as the orbit of the perturbing secondary is approached. However, in reality the width decreases due to the chaotic effect of nearby resonances.

Artificial satellites: Resonance effects produced by terrestrial tide

Effects due to resonances in the orbital motion of artificial satellites disturbed by the terrestrial tide are analyzed. The nodal co-rotation resonance, apsidal co-rotation resonance and the Lidov-Kozai's mechanism are studied. The effects of the resonances are analyzed through the variations of the metric orbital elements. Libration and circulation motions for high orbits with high eccentricities are verified for the Lidov-Kozai's mechanism.

A leitura do fantástico nos contos Ligeia de Edgard Allan Poe, e Véra, de Villiers de L'Isle-Adam

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Dinâmica e origem de asteroides de alta inclinação

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Dinâmica ressonante de alguns satélites artificiais terrestres no sistema Terra-Lua-Sol

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Satélites com alta excentricidade e/ou alta inclinação

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

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

Natural formations at the Earth-Moon triangular point in perturbed restricted problems

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

As cortinas que cerram o Vale: religião e secularização na diocese de Limoeiro do Norte/CE (1940-1980)

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

Multi-planet extrasolar systems - detection and dynamics

20 years after the discovery of the first planets outside our solar system, the current exoplanetary population includes more than 700 confirmed planets around main sequence stars. Approximately 50% belong to multiple-planet systems in very diverse dynamical configurations, from two-planet hierarchical systems to multiple resonances that could only have been attained as the consequence of a smooth large-scale orbital migration. The first part of this paper reviews the main detection techniques employed for the detection and orbital characterization of multiple-planet systems, from the (now) classical radial velocity (RV) method to the use of transit time variations (TTV) for the identification of additional planetary bodies orbiting the same star. In the second part we discuss the dynamical evolution of multi-planet systems due to their mutual gravitational interactions. We analyze possible modes of motion for hierarchical, secular or resonant configurations, and what stability criteria can be defined in each case. In some cases, the dynamics can be well approximated by simple analytical expressions for the Hamiltonian function, while other configurations can only be studied with semi-analytical or numerical tools. In particular, we show how mean-motion resonances can generate complex structures in the phase space where different libration islands and circulation domains are separated by chaotic layers. In all cases we use real exoplanetary systems as working examples.

Tidal perturbations of the rotation of the moon: the creep tide approach

In this communication we report results from the application to the study of the rotation of the Moon of the creeping tide theory just proposed (Ferraz-Mello, Cel. Mech. Dyn. Astron., submitted. ArXiv astro-ph 1204.3957). The choice of the Moon for the first application of this new theory is motivated by the fact that the Moon is one of the best observed celestial bodies and the comparison of the theoretical predictions of the theory with observations i may validate the theory or point out the need of further improvements. Particularly, the tidal perturbations of the rotation of the Moon - the physical libration of the Moon - have been detected in the Lunar Laser Ranging measurements (Williams et al. JGR 106, 27933, 2001). The major difficulty in this application comes from the fact that tidal torques in a planet-satellite system are very sensitive to the distance between the two-bodies, which is strongly affected by Solar perturbations. In the case of the Moon, the main solar perturbations - the Evection and the Variation - are more important than most of the Keplerian oscillations, being smaller only than the first Keplerian harmonic (equation of the centre). Besides, two of the three components of the Moon's libration in longitude whose tidal contributions were determined by LLR are related to these perturbations. The results may allow us to determine the main parameter of a possible Moon's creeping tide. The preliminary results point to a relaxation factor (gamma) 2 to 4 times smaller than the one predicted from the often cited values of thr Moon's quality factor Q (between 30 and 40), and points to larger Q values.

Der Kampf um den 19. März: Zur gesellschaftlichen Auseinandersetzung um das Totengedenken der Algerienkriegsveteranen in Frankreich

Der Beitrag behandelt die Entwicklung der geschichtspolitischen Auseinandersetzungen um den 19. März, den die 'Fédération Nationale des Anciens Combattants en Algérie, Maroc, Tunisie' ( FNACA) als führender Verband der französischen Algerienkriegsveteranen zum Totengedenktag für ihre zwischen 1954 und 1962 gefallenen Kameraden erklärt hat. Der 19. März 1962 steht als Tag des Waffenstillstandes zwischen der französischen Kolonialarmee und der algerischen Nationalen Befreiungsbewegung FLN ('Front de Libération Nationale') für den Frieden in Algerien. Ihm haftet zugleich der Geruch der Kapitulation vor den 'Rebellen' an, da er den Prozess einleitete, der zur Unabhängigkeit Algeriens führte. Die verschiedenen Regierungen der Fünften Republik weigerten sich beharrlich, den 19. März als Feiertag anzuerkennen, da er als Datum zur Aussöhnung der im Algerienkrieg zerrissenen Nation nicht geeignet sei. Stattdessen wurden die von der FNACA organisierten Gedenkaktivitäten seit den 1970er Jahren regelmäßig zur Zielscheibe polemischer Angriffe aus dem Lager jener rechten politischen Kräfte, die weiterhin das Erbe des französischen Kolonialismus in Algerien verteidigten.

Empfehlungen zur Diagnostik und Therapie der behavioralen und psychologischen Symptome der Demenz (BPSD)

In patients with dementia, Behavioral and Psychological Symptoms of Dementia (BPSD) are frequent findings that accompany deficits caused by cognitive impairment and thus complicate diagnostics, therapy and care. BPSD are a burden both for affected individuals as well as care-givers, and represent a significant challenge for therapy of a patient population with high degree of multi-morbidity. The goal of this therapy-guideline issued by swiss professional associations is to present guidance regarding therapy of BPSD as attendant symptoms in dementia, based on evidence as well as clinical experience. Here it appears to be of particular importance to take into account professional experience, as at this point for most therapeutic options no sufficiently controlled clinical trials are available. A critical discussion of pharmaco-therapeutic intervention is necessary, as this patient-population is particularly vulnerable for medication side-effects. Finally, a particular emphasis is placed on incorporating and systematically reporting psycho-social and nursing options therapeutic intervention.