On the scattering of comets by a planet

In this paper, numerical simulations are made, using the three-dimensional restricted three-body problem as the mathematical model, to calculate the effects of a swing-by with the planet Saturn in the orbit of a comet. To show the results, the orbit of the comet is classified in four groups: elliptic direct, elliptic retrograde, hyperbolic direct and hyperbolic retrograde. Then, the modification in the orbit of the comet due to the close approach is shown in plots that specify from which group the comet's orbit is coming and to which group it is going. Several families of orbits are found and shown in detail. An analysis about the trends as parameters (position and velocity at the periapse) vary is performed and the influence of each of them is shown and explained. The result is a collection of maps that describe the evolution of the trajectory of the comet due to the close approach. Those maps can be used to estimate the probability of some events, like the capture or escape of a comet. An example of this technique is shown in the paper. (C) 2005 COSPAR. Published by Elsevier Ltd. All rights reserved.

Z(bus) transmission network cost allocation

This paper addresses the problem of allocating the cost of the transmission network to generators and demands. A physically-based network usage procedure is proposed. This procedure exhibits desirable apportioning properties and is easy to implement and understand. A case study based on the IEEE 24-bus system is used to illustrate the working of the proposed technique. Some relevant conclusions are finally drawn.

Calcaneal apophysitis: a quantitative radiographic evaluation of the secondary ossification center

Background: Calcaneal apophysitis in children is a self-limited condition that may interfere with walking and physical performance in sports, thus causing concern to the patient and parents. There is still controversy about the significance of the radiographic changes in children with heel pain, since the report of Sever in 1912. One of the reasons is that normal children may display a considerable variation in the radiographic aspects of the secondary ossification center of the calcaneus at different ages. Methods: In this investigation, the developmental aspects of primary and secondary ossification centers of the calcaneus were studied in radiographs obtained from healthy boys and from boys with calcaneal apophysitis. The normal population comprised 392 children and adolescents ranging in age from 6 to 15 years. There were 69 individuals with calcaneal apophysitis ranging in age from 8 to 14 years. Lateral standard radiographs were obtained of both heels, and a copper step wedge was used as a calibration to determine bone density. The following parameters were analyzed on the plain films: time of appearance, fusion and number of fragments of the secondary nucleus, area and bone densitometry of the primary and secondary ossification centers of the calcaneus. Results: In the normal population, the ossification of the secondary nucleus began at 7 years of age, and at 15 years of age, the nucleus was fused in all individuals. In the apophysitis group, the secondary ossification center was present and not fused in all individuals. Both secondary nuclei increased in size with age with no difference between the two groups. Regarding bone density, both the primary and secondary nuclei were less dense in the apophysitis group than their counterparts in the normal population. The most significant difference between the two populations referred to the degree of fragmentation, which was greater in the apophysitis group. Conclusion: Our data showed that the sclerotic aspect of the secondary nucleus of the calcaneus is a normal feature and, therefore, should not be used to establish the diagnosis of Sever's disease. The most consistent difference between the normal and apophysitis group was related to the more fragmented aspect of the secondary nucleus in the latter individuals, which may suggest a mechanical etiology for that condition.

Plutonism in three orogenic pulses, Eastern Blue Ridge Province, southern Appalachians

The Eastern Blue Ridge Province of the southern Appalachians contains, in part, remnants of an Ordovician accretionary wedge complex formed during subduction of an oceanic tract before mid-Ordovician accretion with Laurentia. The Eastern Blue Ridge Province consists of metapelite and amphibolite intruded by low-K plutons, high-temperature (T > 750 degrees C) Ordovician eclogite, and other high-pressure metamafic and meta-ultramatic rocks. Felsic plutons in the Eastern Blue Ridge Province are important time markers for regional-scale tectonics, deformation, and metamorphism. Plutons were thought to be related to either Taconian (Ordovician) or Acadian (Devonian-Silurian) tectonothermal events.We dated five plutonic or metaplutonic rocks to constrain pluton crystallization ages better and thus the timing of tectonism. The Persimmon Creek gneiss yielded a protolith crystallization age of 455.7 +/- 2.1 Ma, Chalk Mountain 377.7 +/- 2.5 Ma, Mt. Airy 334 +/- 3 Ma, Stone Mountain 335.6 +/- 1.0 Ma, and Rabun 335.1 +/- 2.8 Ma. The latter four plutons were thought to be part of the Acadian Spruce Pine Suite, but instead our new ages indicate that Alleghanian (Carboniferous-Permian) plutonism is widespread and voluminous in the Eastern Blue Ridge Province. The Chattahoochee fault, which was considered an Acadian structure, cuts the Rabun pluton and thus must have been active during the Alleghanian orogeny. The new ages indicate that Persimmon Creek crystallized less than 3 m.y. after zircon crystallization in Eastern Blue Ridge eclogite and is nearly synchronous with nearby high-grade metamorphism and migmatization. The three phases of plutonism in the Eastern Blue Ridge Province correspond with established metamorphic ages for each of the three major orogenic pulses along the western flank of the southern Appalachians.

A constraints generator in structural determination by microcomputer

We present a new expert system: a constraints generator for structure determination of natural products. The constraints that the system furnishes are: skeleton (reliability: 95%), large substructures (reliability: 98%) and their associated assignments (reliability: 90%) This system is intended for structure determination of carbon-rich compounds (sesqui-, di- and triterpenes, sterols etc.) for which most structures generators are not very effective. We also present a new algorithm that can avoid the combinatorial explosion during subspectrum/substructure analysis.

Mesozoic tectonic evolution of the south Orkney microcontinent, Scotia arc, Antarctica

The South Orkney Islands are the exposed part of a continental fragment on the southern limb of the Scotia are. The islands are to a large extent composed of metapelites and metagreywackes of probable Triassic sedimentary age. Deformation related to an accretionary wedge setting, with associated metamorphism from anchizone to the greenschist facies, are of Jurassic age (176-200 Ma). on Powell Island, in the centre of the archipelago, five phases of deformation are recognized. The first three, associated with the main metamorphism, are tentatively correlated with early Jurassic subduction along the Pacific margin of Gondwana. D-4 is a phase of middle to late Jurassic crustal extension associated with uplift. This extension phase may be related to opening of the Rocas Verdes basin in southern Chile, associated with the breakup of Gondwanaland. Upper Jurassic conglomerates cover the metamorphic rocks unconformably. D-5 is a phase of brittle extensional faulting probably associated with Cenozoic opening of the Powell basin west of the archipelago, and with development of the Scotia are.

Allocation of the costs of transmission losses

An analysis of the performance of six major methods of loss allocation for generators and demands was conducted, based on pro-rata (two), on incremental factors (two), on proportional sharing (PS) (one), and on electric circuit theory (one). Using relatively simple examples which can easily be checked, the advantages and disadvantages of each were ascertained and the results confirmed using a larger sample system (IEEE-118). The discussion considers the location and size of generators and demands, as well as the merits of the location of these agents for each configuration based on an analysis of the effect of various network modifications. Furthermore, an application in the South-Southeastern Brazilian Systems is performed. Conclusions and recommendations are presented. (C) 2004 Elsevier B.V. All rights reserved.

Analytical attitude propagation with non-singular variables and gravity gradient torque for spin stabilized satellite

An analytical approach for the spin stabilized satellite attitude propagation is presented using the non-singular canonical variables to describe the rotational motion. Two sets of variables were introduced for Fukushima in 1994 by a canonical transformation and they are useful when the angle between z-satellite axis of a coordinate system fixed in artificial satellite and the rotational angular momentum vector is zero or when the angle between Z-equatorial axis and rotation angular momentum vector is zero. Analytical solutions for rotational motion equations and torque-free motion are discussed in terms of the elliptic functions and by the application of some simplification to get an approximated solution. These solutions are compared with a numerical solution and the results show a good agreement for many rotation periods. When the mean Hamiltonian associated with the gravity gradient torque is included, an analytical solution is obtained by the application of the successive approximations' method for the satellite in an elliptical orbit. These solutions show that the magnitude of the rotation angular moment is not affected by the gravity gradient torque but this torque causes linear and periodic variations in the angular variables, long and short periodic variations in Z-equatorial component of the rotation angular moment and short periodic variations in x-satellite component of the rotation angular moment. The goal of this analysis is to emphasize the geometrical and physical meaning of the non-singular variables and to validate the approximated analytical solution for the rotational motion without elliptic functions for a non-symmetrical satellite. The analysis can be applied for spin stabilized satellite and in this case the general solution and the approximated solution are coincidence. Then the results can be used in analysis of the space mission of the Brazilian Satellites. (C) 2007 COSPAR. Published by Elsevier Ltd. All rights reserved.

Effects of the eccentricity on the primaries in the gravitational capture phenomenon

Gravitational capture is a characteristic of some dynamical systems in celestial mechanics, as in the elliptic restricted three-body problem that is considered in this paper. The basic idea is that a spacecraft (or any particle with negligible mass) can change a hyperbolic orbit with a small positive energy around a celestial body into an elliptic orbit with a small negative energy without the use of any propulsive system. The force responsible for this modification in the orbit of the spacecraft is the gravitational force of the third body involved in the dynamics. In this way, this force is used as a zero cost control, equivalent to a continuous thrust applied in the spacecraft. One of the most important applications of this property is the construction of trajectories to the Moon. The objective of the present paper is to study in some detail the effects of the eccentricity of the primaries in this maneuver.

Peculiar trajectories around the Lagrangian equilateral points

In the present work we analyse the behaviour of a particle under the gravitational influence of two massive bodies and a particular dissipative force. The circular restricted three body problem, which describes the motion of this particle, has five equilibrium points in the frame which rotates with the same angular velocity as the massive bodies: two equilateral stable points (L-4, L-5) and three colinear unstable points (L-1, L-2, L-3). A particular solution for this problem is a stable orbital libration, called a tadpole orbit, around the equilateral points. The inclusion of a particular dissipative force can alter this configuration. We investigated the orbital behaviour of a particle initially located near L4 or L5 under the perturbation of a satellite and the Poynting-Robertson drag. This is an example of breakdown of quasi-periodic motion about an elliptic point of an area-preserving map under the action of dissipation. Our results show that the effect of this dissipative force is more pronounced when the mass of the satellite and/or the size of the particle decrease, leading to chaotic, although confined, orbits. From the maximum Lyapunov Characteristic Exponent a final value of gamma was computed after a time span of 10(6) orbital periods of the satellite. This result enables us to obtain a critical value of log y beyond which the orbit of the particle will be unstable, leaving the tadpole behaviour. For particles initially located near L4, the critical value of log gamma is -4.07 and for those particles located near L-5 the critical value of log gamma is -3.96. (c) 2006 Elsevier B.V. All rights reserved.

Three-body problem, its Lagrangian points and how to exploit them using an alternative transfer to L4 and L5

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

An approach of optimal sensitivity applied in the tertiary loop of the automatic generation control

This paper proposes an approach of optimal sensitivity applied in the tertiary loop of the automatic generation control. The approach is based on the theorem of non-linear perturbation. From an optimal operation point obtained by an optimal power flow a new optimal operation point is directly determined after a perturbation, i.e., without the necessity of an iterative process. This new optimal operation point satisfies the constraints of the problem for small perturbation in the loads. The participation factors and the voltage set point of the automatic voltage regulators (AVR) of the generators are determined by the technique of optimal sensitivity, considering the effects of the active power losses minimization and the network constraints. The participation factors and voltage set point of the generators are supplied directly to a computational program of dynamic simulation of the automatic generation control, named by power sensitivity mode. Test results are presented to show the good performance of this approach. (C) 2008 Elsevier B.V. All rights reserved.

Dynamical capture in the Pluto-Charon system

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Strategies for plane change of Earth orbits using lunar gravity and derived trajectories of family G

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Conchostráceos com linhas de crescimento recurvadas junto à margem dorsal (famílias Palaeolimnadiopseidae e Perilimnadiidae) da formação rio do rasto, Permiano superior, bacia do Paraná, Brasil

Some Upper Permian conchostracans from the Rio do Rasto Formation (Parana Basin, South Brazil) have very characteristic recurved growth lines at the dorsal margin. All previously described specimens were classified as Palaeolimnadiopsis subalata (Reed) Raymond. However, a re-analysis of these fossils and of additional recently- collected specimens demonstrated that not all can be included in a single species, nor only in the Family Palaeolimnadiopseidae. According to their shape and the size of the umbo, they are classified into three species. The sub-elliptic carapaces with small anterior umbo are maintained in Palaeolimnadiopsis subalata (Reed, 1929) Raymond, 1946. The sub-circular carapaces with small sub-central umbo correspond to the new species Palaeolimnadiopsis riorastensis. The small size of the umbo is a character of the Family Palaeolimnadiopseidae. The small elliptic valves with large anterior umbo are assigned to the new species Falsisca brasiliensis of the Family Perilimnadiidae, which is characterized by large umbos. Palaeolimnadiopsis has a wide chronostratigraphic distribution, but Falsisca is restricted to the Upper Permian-Lower Triassic of Europe and Asia. This interval is in agreement with the probable Late Permian age of the respective strata of the Rio do Rasto formation. Falsisca was not previously recorded in Gondwana.