A new set of integrals of motion to propagate the perturbed two-body problem

A formulation of the perturbed two-body problem that relies on a new set of orbital elements is presented. The proposed method represents a generalization of the special perturbation method published by Peláez et al. (Celest Mech Dyn Astron 97(2):131?150,2007) for the case of a perturbing force that is partially or totally derivable from a potential. We accomplish this result by employing a generalized Sundman time transformation in the framework of the projective decomposition, which is a known approach for transforming the two-body problem into a set of linear and regular differential equations of motion. Numerical tests, carried out with examples extensively used in the literature, show the remarkable improvement of the performance of the new method for different kinds of perturbations and eccentricities. In particular, one notable result is that the quadratic dependence of the position error on the time-like argument exhibited by Peláez?s method for near-circular motion under the J2 perturbation is transformed into linear.Moreover, themethod reveals to be competitive with two very popular elementmethods derived from theKustaanheimo-Stiefel and Sperling-Burdet regularizations

Linear stability of periodic three-body orbits with zero angular momentum and topological dependence of Kepler's third law: a numerical test

We test numerically the recently proposed linear relationship between the scale-invariant period Ts.i. = T|E| 3/2, and the topology of an orbit, on several hundred planar Newtonian periodic three-body orbits. Here T is the period of an orbit, E is its energy, so that Ts.i. is the scale-invariant period, or, equivalently, the period at unit energy |E| = 1. All of these orbits have vanishing angular momentum and pass through a linear, equidistant configuration at least once. Such orbits are classified in ten algebraically well-defined sequences. Orbits in each sequence follow an approximate linear dependence of Ts.i., albeit with slightly different slopes and intercepts. The orbit with the shortest period in its sequence is called the ‘progenitor’: six distinct orbits are the progenitors of these ten sequences. We have studied linear stability of these orbits, with the result that 21 orbits are linearly stable, which includes all of the progenitors. This is consistent with the Birkhoff–Lewis theorem, which implies existence of infinitely many periodic orbits for each stable progenitor, and in this way explains the existence and ensures infinite extension of each sequence

Histology of the Pharyngeal Constrictor Muscle in 22q11.2 Deletion Syndrome and Non-Syndromic Children with Velopharyngeal Insufficiency

Plastic surgeons aim to correct velopharyngeal insufficiency manifest by hypernasal speech with a velopharyngoplasty. The functional outcome has been reported to be worse in patients with 22q11.2 deletion syndrome than in patients without the syndrome. A possible explanation is the hypotonia that is often present as part of the syndrome. To confirm a myogenic component of the etiology of velopharyngeal insufficiency in children with 22q11.2 deletion syndrome, specimens of the pharyngeal constrictor muscle were taken from children with and without the syndrome. Histologic properties were compared between the groups. Specimens from the two groups did not differ regarding the presence of increased perimysial or endomysial space, fiber grouping by size or type, internalized nuclei, the percentage type I fibers, or the diameters of type I and type II fibers. In conclusion, a myogenic component of the etiology of velopharyngeal insufficiency in children with 22q11.2 deletion syndrome could not be confirmed

Thermodynamic Assessment of the Cu-Pt System

A CALPHAD assessment of the Cu-Pt system has been carried out. Two and four sublattice models were applied to describe the Gibbs free energies of ordered phases where the contribution of SRO is taken explicitly into account through the reciprocal parameters. The disordered fcc A1 and liquid phases were treated as substitutional solutions. A consistent set of parameters for the phases in the Cu-Pt system as obtained, and those parameters can satisfactorily reproduce the experimental phase equilibria and thermodynamic properties, such as enthalpies, activity of Cu, and long-range order parameters