Caustics of the restricted three-body problem

Trajectories of the planar, circular, restricted three-body problem are given in the configuration space through the caustics associated to the invariant tori of quasi-periodic orbits. It is shown that the caustics of trajectories librating in any particular resonance display some features associated to that resonance. This method can be considered complementary to the Poincare surface of section method, because it provides information not accessible by the other method.

Experimental and theoretical study of the ferroelectric and piezoelectric behavior of strontium-doped PZT

Theoretical data using ab initio perturbed ion calculation were compared with ferroelectric and piezoelectric experimental data of strontium doped PZT. Various concentrations of SrO in PZT at constant temperature and sintering time were carried out. Experimental results, such as the remanent polarization, P-R of 6.9-8.9 muC/Cm-2, the coercive field, E-C of 6.6-7.8 kVcm, and the planar coupling factor, Kp of 0.45-0.53, were compared with the energy of Zr4+ and Ti4+ ion dislocation and the lattice interaction energy which show that strontium increment in PZT alter the energies and increase the values of piezoelectric and ferroelectric variables. Calculations of lattice energy of the rhombohedral phase show that a phase non-stability is coincident with increasing experimental values of the P-R, E-C and Kp. (C) 2001 Elsevier B.V. Ltd. All rights reserved.