Manuel Iñarrea

CHAOS IN THE REORIENTATION PROCESS OF A DUAL-SPIN SPACECRAFT WITH TIME-DEPENDENT MOMENTS OF INERTIA

We study the spin-up dynamics of a dual-spin spacecraft containing one axisymmetric rotor which is parallel to one of the principal axes of the spacecraft. It will be supposed that one of the moments of inertia of the platform is a periodic function of time and that the center of mass of the spacecraft is not modified. Under these assumptions, it is shown that in the absence of external torques and spinning rotors the system possesses chaotic behavior in the sense that it exhibits Smales horseshoes. We prove this statement by means of the Melnikov method. The presence of chaotic behavior results in a random spin-up operation. This randomness is visualized by means of maps of the initial conditions with final nutation angle close to zero. This phenomenon is well described by a suitable parameter that measures the amount of randomness of the process. Finally, we relate this parameter with the Melnikov function in the absence of the spinning rotor and with the presence of subharmonic resonances.

Spin Rotor Stabilization of a Dual-Spin Spacecraft with Time Dependent Moments of Inertia

We consider a dual-spin deformable spacecraft, in the sense that one of the moments of inertia is a periodic function of time such that the center of mass is not altered. In the absence of external torques and spin rotors, by means of the Melnikovs method we prove that the body motion is chaotic. Stabilization is obtained by means of a spinning rotor about one of the principal axes of inertia.

Libration Control of Electrodynamic Tethers Using the Extended Time-Delayed Autosynchronization Method

Any electrodynamic tether working in an inclined orbit is affected by a dynamic instability generated by the continuous pumping of energy from electromagnetic forces into the tether attitude motion. In order to overcome the difficulties associated with this instability, a new control scheme has been analyzed in this paper. The background strategy is as follows: we add appropriate forces to the system with the aim of converting an unstable periodic orbit of the governing equations into an asymptotically stable one. The idea is to take such a stabilized periodic orbit as the starting point for the operation of the electrodynamic tether. We use an extended delay feedback control scheme which has been used successfully in problems with one degree of freedom. In order to obtain results with broad validity, some simplifying assumptions have been introduced in the analysis. Thus, we assume a rigid tether with two end masses orbiting along a circular, inclined orbit. We also assume a constant tether current which does not depend on the attitude and orbital position of the tether. The Earth’s magnetic field is modeled as a dipole aligned with the Earth’s rotation axis.

Chaotic Rotations of an Asymmetric Body with Time-Dependent Moments of Inertia and Viscous Drag

We study the dynamics of a rotating asymmetric body under the influence of an aerodynamic drag. We assume that the drag torque is proportional to the angular velocity of the body. Also we suppose that one of the moments of inertia of the body is a periodic function of time and that the center of mass of the body is not modified. Under these assumptions, we show that the system exhibits a transient chaotic behavior by means of a higher dimensional generalization of the Melnikovs method. This method give us an analytical criterion for heteroclinic chaos in terms of the system parameters. These analytical results are confirmed by computer numerical simulations of the system rotations.

Bifurcations of dividing surfaces in chemical reactions.

We study the dynamical behavior of the unstable periodic orbit (NHIM) associated to the non-return transition state (TS) of the H(2) + H collinear exchange reaction and their effects on the reaction probability. By means of the normal form of the Hamiltonian in the vicinity of the phase space saddle point, we obtain explicit expressions of the dynamical structures that rule the reaction. Taking advantage of the straightforward identification of the TS in normal form coordinates, we calculate the reaction probability as a function of the system energy in a more efficient way than the standard Monte Carlo method. The reaction probability values computed by both methods are not in agreement for high energies. We study by numerical continuation the bifurcations experienced by the NHIM as the energy increases. We find that the occurrence of new periodic orbits emanated from these bifurcations prevents the existence of a unique non-return TS, so that for high energies, the transition state theory cannot be longer applied to calculate the reaction probability.

Stability of the permanent rotations of an asymmetric gyrostat in a uniform Newtonian field

The stability of the permanent rotations of a heavy gyrostat is analyzed by means of the Energy-Casimir method. Sufficient and necessary conditions are established for some of the permanent rotations. The geometry of the gyrostat and the value of the gyrostatic moment are relevant in order to get stable permanent rotations. Moreover, the necessary conditions are also sufficient, for some configurations of the gyrostat.

Lyapunov stability for a generalized Hénon-Heiles system in a rotating reference frame

In this paper we focus on a generalized Henon-Heiles system in a rotating reference frame, in such a way that Lagrangian-like equilibrium points appear. Our goal is to study their nonlinear stability properties to better understand the dynamics around these points. We show the conditions on the free parameters to have stability and we prove the superstable character of the origin for the classical case; it is a stable equilibrium point regardless of the frequency value of the rotating frame.

Nonlinear dynamics of atoms in a crossed optical dipole trap.

We explore the classical dynamics of atoms in an optical dipole trap formed by two identical Gaussian beams propagating in perpendicular directions. The phase space is a mixture of regular and chaotic orbits, the latter becoming dominant as the energy of the atoms increases. The trapping capabilities of these perpendicular Gaussian beams are investigated by considering an atomic ensemble in free motion. After a sudden turn on of the dipole trap, a certain fraction of atoms in the ensemble remains trapped. The majority of these trapped atoms has energies larger than the escape channels, which can be explained by the existence of regular and chaotic orbits with very long escape times.

Rydberg hydrogen atom near a metallic surface : Stark regime and ionization dynamics

We investigate the classical dynamics of a hydrogen atom near a metallic surface in the presence of a uniform electric field. To describe the atom-surface interaction we use a simple electrostatic image model. Owing to the axial symmetry of the system, the z-component of the canonical angular momentum P{sub {phi}} is an integral and the electronic dynamics is modeled by a two degrees of freedom Hamiltonian in cylindrical coordinates. The structure and evolution of the phase space as a function of the electric field strength is explored extensively by means of numerical techniques of continuation of families of periodic orbits and Poincare surfaces of section. We find that, due to the presence of the electric field, the atom is strongly polarized through two consecutive pitchfork bifurcations that strongly change the phase space structure. Finally, by means of the phase space transition state theory and the classical spectral theorem, the ionization dynamics of the atom is studied.

Analysis of the classical phase space and energy transfer for two rotating dipoles with and without external electric field

We explore the classical dynamics of two interacting rotating dipoles that are fixed in the space and exposed to an external homogeneous electric field. Kinetic energy transfer mechanisms between the dipoles are investigated by varying both the amount of initial excess kinetic energy of one of them and the strength of the electric field. In the field-free case, and depending on the initial excess energy, an abrupt transition between equipartition and nonequipartition regimes is encountered. The study of the phase space structure of the system as well as the formulation of the Hamiltonian in an appropriate coordinate frame provide a thorough understanding of this sharp transition. When the electric field is turned on, the kinetic energy transfer mechanism is significantly more complex and the system goes through different regimes of equipartition and nonequipartition of the energy including chaotic behavior.