Periodic orbits of the planar collision restricted 3-body problem

Using the continuation method we prove that the circular and the elliptic symmetric periodic orbits of the planar rotating Kepler problem can be continued into periodic orbits of the planar collision restricted 3–body problem. Additionally, we also continue to this restricted problem the so called “comets orbits”.

GNSS array: diseño de una antena con polarización circular

Aquest projecte es centra en el disseny d’una antena microstrip per a GNSS. Una antena per a GNSS ha de tenir adaptació de impedància d’entrada i polarització circular a dretes, com a principals especificacions, en el rang de 1.15-1.6 GHz. El tipus d’alimentació d’una antena microstrip amb el major ample de banda d’adaptació és l’alimentació mitjançant acoblament per apertura. Si a l’antena s’introdueixen dos apertures de forma ortogonal, alimentades amb un desfasament de 90º entre elles, s’aconsegueix polarització circular. L’opció de separar les apertures redueix la transferència de potència entre elles, i disminueix el guany de polarització creuada. La xarxa d’alimentació dissenyada és un divisor de Wilkinson amb una línia de λ/4 a la freqüència central, encara que el desfasament als extrems de la banda no sigui de 90º. Com a xarxa d’alimentació es va provar un hibrid de 90º, però l’elevat valor del paràmetre S21 de l’antena impossibilita l’adaptació a l’entrada del hibrid.

Chiroptical measurement of chiral aggregates at liquid-liquid interface in centrifugal liquid membrane cell by Mueller matrix and conventional circular dichroism methods

The centrifugal liquid membrane (CLM) cell has been utilized for chiroptical studies of liquid-liquid interfaces with a conventional circular dichroism (CD) spectropolarimeter. These studies required the characterization of optical properties of the rotating cylindrical CLM glass cell, which was used under the high speed rotation. In the present study, we have measured the circular and linear dichroism (CD and LD) spectra and the circular and linear birefringence (CB and LB) spectra of the CLM cell itself as well as those of porphyrine aggregates formed at the liquid-liquid interface in the CLM cell, applying Mueller matrix measurement method. From the results, it was confirmed that the CLM-CD spectra of the interfacial porphyrin aggregates observed by a conventional CD spectropolarimeter should be correct irrespective of LD and LB signals in the CLM cell.

Families of periodic orbits for the spatial isosceles 3-body problem

We study the families of periodic orbits of the spatial isosceles 3-body problem (for small enough values of the mass lying on the symmetry axis) coming via the analytic continuation method from periodic orbits of the circular Sitnikov problem. Using the first integral of the angular momentum, we reduce the dimension of the phase space of the problem by two units. Since periodic orbits of the reduced isosceles problem generate invariant two-dimensional tori of the nonreduced problem, the analytic continuation of periodic orbits of the (reduced) circular Sitnikov problem at this level becomes the continuation of invariant two-dimensional tori from the circular Sitnikov problem to the nonreduced isosceles problem, each one filled with periodic or quasi-periodic orbits. These tori are not KAM tori but just isotropic, since we are dealing with a three-degrees-of-freedom system. The continuation of periodic orbits is done in two different ways, the first going directly from the reduced circular Sitnikov problem to the reduced isosceles problem, and the second one using two steps: first we continue the periodic orbits from the reduced circular Sitnikov problem to the reduced elliptic Sitnikov problem, and then we continue those periodic orbits of the reduced elliptic Sitnikov problem to the reduced isosceles problem. The continuation in one or two steps produces different results. This work is merely analytic and uses the variational equations in order to apply Poincar´e’s continuation method.