J. P. Salas

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.

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.

Perturbed ion traps: A generalization of the three-dimensional Hénon–Heiles problem

This paper presents an analytical study of an axially symmetric perturbation of the Penning trap. This system is modeled as a generalization of the three-dimensional (3D) Henon-Heiles potential. Thus, the same techniques which succeeded in the study of the 3D Henon-Heiles system apply here. The departure Hamiltonian is three dimensional, although it possesses an axial symmetry. This property, together with an averaging process, is used to reduce the original system to an integrable one. We study the flow of the reduced Hamiltonian: equilibria, bifurcations, and stability, extracting thereafter the relevant information about the dynamics of the original problem. (c) 2002 American Institute of Physics.

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.