Non-integrability of the problem of a rigid satellite in gravitational and magnetic fields

In this paper we analyse the integrability of a dynamical system describing the rotational motion of a rigid satellite under the influence of gravitational and magnetic fields. In our investigations we apply an extension of the Ziglin theory developed by Morales-Ruiz and Ramis. We prove that for a symmetric satellite the system does not admit an additional real meromorphic first integral except for one case when the value of the induced magnetic moment along the symmetry axis is related to the principal moments of inertia in a special way.Comment: 39 pages, 4 figures, missing bibliography was adde

Quasilinear theory of collisionless Fermi acceleration in a multicusp magnetic confinement geometry

Particle motion in a cylindrical multiple-cusp magnetic field configuration is shown to be highly (though not completely) chaotic, as expected by analogy with the Sinai billiard. This provides a collisionless, linear mechanism for phase randomization during monochromatic wave heating. A general quasilinear theory of collisionless energy diffusion is developed for particles with a Hamiltonian of the form $H_0+H_1$, motion in the \emph{unperturbed} Hamiltonian $H_0$ being assumed chaotic, while the perturbation $H_1$ can be coherent (i.e. not stochastic). For the multicusp geometry, two heating mechanisms are identified --- cyclotron resonance heating of particles temporarily mirror-trapped in the cusps, and nonresonant heating of nonadiabatically reflected particles (the majority). An analytically solvable model leads to an expression for a transit-time correction factor, exponentially decreasing with increasing frequency. The theory is illustrated using the geometry of a typical laboratory experiment.Comment: 13 pages (.tex file, using REVTeX), 11 figures (.eps files). Sep. 30: Word "collisionless" added to title, abstract and text slightly revised in response to referee's comments (to be published in Phys. Rev. E

A Unification of Models of Tethered Satellites

In this paper, different conservative models of tethered satellites are related mathematically, and it is established in what limit they may provide useful insight into the underlying dynamics. An infinite dimensional model is linked to a finite dimensional model, the slack-spring model, through a conjecture on the singular perturbation of tether thickness. The slack-spring model is then naturally related to a billiard model in the limit of an inextensible spring. Next, the motion of a dumbbell model, which is lowest in the hierarchy of models, is identified within the motion of the billiard model through a theorem on the existence of invariant curves by exploiting Moser's twist map theorem. Finally, numerical computations provide insight into the dynamics of the billiard model

Hot Jupiters and stellar magnetic activity

Recent observations suggest that stellar magnetic activity may be influenced by the presence of a close-by giant planet. Specifically, chromospheric hot spots rotating in phase with the planet orbital motion have been observed during some seasons in a few stars harbouring hot Jupiters. The spot leads the subplanetary point by a typical amount of about 60-70 degrees, with the extreme case of upsilon And where the angle is about 170 degrees. The interaction between the star and the planet is described considering the reconnection between the stellar coronal field and the magnetic field of the planet. Reconnection events produce energetic particles that moving along magnetic field lines impact onto the stellar chromosphere giving rise to a localized hot spot. A simple magnetohydrostatic model is introduced to describe the coronal magnetic field of the star connecting its surface to the orbiting planet. The field is assumed to be axisymmetric around the rotation axis of the star and its configuration is more general than a linear force-free field. With a suitable choice of the free parameters, the model can explain the phase differences between the hot spots and the planets observed in HD 179949, upsilon And, HD 189733, and tau Bootis, as well as their visibility modulation on the orbital period and seasonal time scales. The possible presence of cool spots associated with the planets in tau Boo and HD 192263 cannot be explained by the present model. However, we speculate about the possibility that reconnection events in the corona may influence subphotospheric dynamo action in those stars producing localized photospheric (and chromospheric) activity migrating in phase with their planets.Comment: 9 pages, 5 figures, 2 tables, 2 appendixes, accepted by Astronomy & Astrophysic

Chaotic dynamics of a spinless axisymmetric extended body around a Schwarzschild black hole

We investigate the long-term orbital dynamics of spinless extended bodies in Schwarzschild geometry, and show that periodic deviations from spherical symmetry in the shape of a test body may trigger the onset of chaos. We do this by applying Dixon's formalism at quadrupolar order to a nearly spherical body whose shape oscillates between a prolate and an oblate spheroid. The late-time chaotic behavior is then verified by applying Melnikov's method.Comment: 8 pages, 3 figures. To appear in Phys Rev

The Physical Role of Gravitational and Gauge Degrees of Freedom in General Relativity - I: Dynamical Synchronization and Generalized Inertial Effects

This is the first of a couple of papers in which, by exploiting the capabilities of the Hamiltonian approach to general relativity, we get a number of technical achievements that are instrumental both for a disclosure of \emph{new} results concerning specific issues, and for new insights about \emph{old} foundational problems of the theory. The first paper includes: 1) a critical analysis of the various concepts of symmetry related to the Einstein-Hilbert Lagrangian viewpoint on the one hand, and to the Hamiltonian viewpoint, on the other. This analysis leads, in particular, to a re-interpretation of {\it active} diffeomorphisms as {\it passive and metric-dependent} dynamical symmetries of Einstein's equations, a re-interpretation which enables to disclose the (nearly unknown) connection of a subgroup of them to Hamiltonian gauge transformations {\it on-shell}; 2) a re-visitation of the canonical reduction of the ADM formulation of general relativity, with particular emphasis on the geometro-dynamical effects of the gauge-fixing procedure, which amounts to the definition of a \emph{global (non-inertial) space-time laboratory}. This analysis discloses the peculiar \emph{dynamical nature} that the traditional definition of distant simultaneity and clock-synchronization assume in general relativity, as well as the {\it gauge relatedness} of the "conventions" which generalize the classical Einstein's convention.Comment: 45 pages, Revtex4, some refinements adde