Limit cycles for singular perturbation problems via inverse integrating factor

In this paper singularly perturbed vector fields Xε defined in ℝ2 are discussed. The main results use the solutions of the linear partial differential equation XεV = div(Xε)V to give conditions for the existence of limit cycles converging to a singular orbit with respect to the Hausdorff distance. © SPM.

Interplanetary natural routes via Moon and Lagrangiam points L1 and L2

Swing-by techniques are extensively used in interplanetary missions to minimize fuel consumption and to raise payloads of spaceships. The effectiveness of this type of maneuver has been proven since the beginning of space exploration. According to this premise, we have explored the existence of a natural and direct links between low Earth orbits and the lunar sphere of influence, to obtain low-energy interplanetary trajectories through swing-bys with the Moon and the Earth. The existence of these links are related to a family of retrograde periodic orbits around the Lagrangian equilibrium point L1 predicted for the circular, planar, restricted three-body Earth-Moon-particle problem. The trajectories in these links are sensitive to small disturbances. This enables them to be conveniently diverted reducing so the cost of the swing-by maneuver. These maneuvers allow us a gain in energy sufficient for the trajectories to escape from the Earth-Moon system and to stabilize in heliocentric orbits between the Earth and Venus or Earth and Mars. On the other hand, still within the Earth sphere of influence, and taking advantage of the sensitivity of the trajectories, is possible to design other swing-bys with the Earth or Moon. This allows the trajectories to have larger reach, until they can reach the orbit of other planets as Venus and Mars.(3σ)Broucke, R.A., Periodic Orbits in the Restricted Three-Body Problem with Earth-Moon Masses, JPL Technical Report 32-1168, 1968.

A study of the relative velocities of small particles that are orbiting the earth

The evolution of the velocity of the particles with respect to the circular orbits of satellites that are around the Earth that the particles will cross, suggests a range of possible velocities of impact as a function of the altitude of the satellite. A study made from those results show that the maximum relative velocities occur at the semi-latus rectum, independent of the initial semi-major axis of the particle. Considering both the solar radiation pressure and the oblateness of the Earth, it is visible that a precession in the orbit occurs and there is also a variation in the eccentricity of the particle as a function of its orbital region and its size. This is important information, because the damage caused in a spacecraft depends on the impact velocity.

Third-body perturbation in the case of elliptic orbits for the disturbing body

In the present work it is presented a semi-analytical and a numerical study of the perturbation caused in a spacecraft by a third body using a double averaged analytical model with the disturbing function expanded in Legendre polynomials up to the second-order. The important reason for this procedure is to eliminate the terms due to the short time periodic motion of the spacecraft and to show smooth curves for the evolution of the mean orbital elements for a long time period. The aim of this study is to calculate the effect of lunar perturbations on the orbits of spacecrafts that are traveling around the Earth. It is presented an analysis of the stability of a near-circular orbit and a study to know under which conditions this orbit remains near-circular. A study of the equatorial orbits is also performed.

Autologous orbicularis muscle for filling facial foldsan experimental and clinical study

Purpose: To present a technique for filling facial folds by using autologous orbicularis oculi muscle, based on an experimental model. Methods: two studies are presented: (1) an experimental study using 15 albino guinea-pigs from which a strip of the sural triceps muscle was removed and implanted in the subcutaneous tissue of the dorsal area. The animals were sacrificed 7, 30 and 60 days after the implantation, and the material was histologically evaluated. And (2%) an interventional prospective clinical trial carried out on 20 patients referred to blepharoplasty surgery. They received autologous preseptal orbicularis muscle for filling facial folds. The results where evaluated by patients satisfaction and clinical exam. Results: the sural tricep muscle, when implanted in the subcutaneous tissue, resulted in fibrosis. The patients whom received autologous orbicularis muscle implanted for filling facial folds showed that the procedure can be successfully carried out. Conclusions: autologous preseptal orbicularis muscle is a good material for filling facial folds. Cicatricial tissue will be formed on its implantation site, filling the tissue gap that forms the folds on the skin.

Swarm control designs applied to a micro-electro-mechanical gyroscope system (MEMS)

This paper analyzes the non-linear dynamics of a MEMS Gyroscope system, modeled with a proof mass constrained to move in a plane with two resonant modes, which are nominally orthogonal. The two modes are ideally coupled only by the rotation of the gyro about the plane's normal vector. We demonstrated that this model has an unstable behavior. Control problems consist of attempts to stabilize a system to an equilibrium point, a periodic orbit, or more general, about a given reference trajectory. We also developed a particle swarm optimization technique for reducing the oscillatory movement of the nonlinear system to a periodic orbit. © 2010 Springer-Verlag.

Orbitoethmoidal impacted injury by kitchen knife causing abducens nerve palsy

Introduction: Impacted knife injuries in the maxillofacial region are rare and infrequently reported. In cases of injury involving orbit or eye, these reports are even rarer. Discussion: Damage to the orbital contents may result in a rupture of the globe, extraocular muscle injury, lacrimal gland damage, and others. Orbital foreign bodies are not only difficult to detect, and clinical features vary according to its size, characteristics, shape, penetrating method, and site. In this report, a case of abducens nerve palsy after orbitoethmoidal knife injury is presented. © 2010 Springer-Verlag.

ASTER: A Brazilian mission to an asteroid

The first Brazilian mission to an asteroid is being planned. The target is the asteroid 2001 SN263, which has a NEA orbit of class AMOR. Spectral analysis indicated that this is a C-type asteroid. This type of asteroids are dark and difficult to be studied from Earth. They hold clues of the initial stages of planetary formation and also the origin of water and life on Earth. In fact, radar data showed that 2001 SN263 is composed of three bodies with diameters of about 2.8 km, 1.1 km and 0.4 km. Therefore, the spacecraft will have the opportunity to explore three bodies on the same trip. The mission is scheduled to be launched in 2015, reaching the asteroid in 2018. It will be used a small spacecraft (150 kg) with 30 kg for the payload. The set of scientific instruments being considered to explore the target of this mission include an Imaging Camera, a Laser Rangefinder, an Infrared Spectrometer, a Synthetic Aperture Radar and a Mass Spectrometer. The main measurements to be made include the bulk properties (size, shape, mass, density, dynamics, spin state), the internal properties (structure, gravity field) and surface properties (mineralogy, morphology, elemental composition). The mission also opens an opportunity for some relevant experiments, not directly related to the target. Two such experiments will take benefit from being on board of the spacecraft along the journey to the asteroid system, which will take about three years. The first is an astrobiology experiment. The main goal of this experiment is to determine the viability of the microorganisms survival in extraterrestrial environments simulated in laboratory (chemical atmosphere, temperature, desiccation, vacuum, microgravity and radiation). The second experiment is a plasma package. The main objectives of this experiment are to study the structure and electrodynamics of plasma along the trajectory, the plasma instability processes and the density and temperature of plasma of solar wind origin along the trajectory and near the asteroids. This mission represents a great challenge for the Brazilian space program. It is being structured to allow the full engagement of the Brazilian universities and technological companies in all the necessary developments to be carried out. In this paper, we present some aspects of this mission and details of the payload that will be used and the scientific expectations. Copyright ©2010 by the International Astronautical Federation. All rights reserved.

The aster mission: Exploring for the first time a triple system asteroid

2001 SN263 is a triple system asteroid. Although it was discovery in 2001, in 2008 astronomical observation carried out by Arecibo observatory revealed that it is actually a system with three bodies orbiting each other. The main central body is an irregular object with a diameter about 2.8 km, while the other two are small objects with less than 1 km across. This system presents an orbital eccentricity of 0.47, with perihelion of 1.04 and aphelion of 1.99, which means that it can be considered as a Near Earth Object. This interesting system was chosen as the target for the Aster mission - first Brazilian space exploration undertaking. A small spacecraft with 150 kg of total mass, 30 kg of payload with 110 W available for the instruments, is scheduled to be launched in 2015, and in 2018 it will approach and will be put in orbit of the triple system. This spacecraft will use electric propulsion and in its payload it will carry image camera, laser rangefinder, infrared spectrometer, mass spectrometer, and experiments to be performed in its way to the asteroid. This mission represents a great challenge for the Brazilian space program. It is being structured to allow the full engagement of the Brazilian universities and technological companies in all the necessary developments to be carried out. In this paper, we present some aspects of this mission, including the transfer trajectories to be used, and details of buss and payload subsystems that are being developed and will be used. Copyright ©2010 by the International Astronautical Federation. All rights reserved.

Influence of nonsphericity of planetary satellites and perturbation of the third-body on the artificial satellites motion

Some orbital characteristics of lunar artificial satellites is presented taking into account the perturbation of the third-body in elliptical orbit and the non-uniform distribution of mass of the Moon. We consider the development of the non-sphericity of the Moon in zonal spherical harmonics up to the ninth order and sectorial harmonic C 22 due to the lunar equatorial ellipticity. The motion of the artificial satellite is studied under the single-averaged analytical model. The average is applied to the mean anomaly of the satellite to analyze low-altitude orbits which are of highest importance for future lunar missions. We found families of frozen orbits with long lifetimes for the problem of an orbiter travelling around the Moon.

Optimal low cost transfer to L4 and L5 lagrangian points

Lagrangian points L4 and L5 lie at 60 degrees ahead of and behind Moon in its orbit with respect to the Earth. Each one of them is a third point of an equilateral triangle with the base of the line defined by those two bodies. These Lagrangian points are stable for the Earth-Moon mass ratio. Because of their distance electromagnetic radiations from the Earth arrive on them substantially attenuated. As so, these Lagrangian points represent remarkable positions to host astronomical observatories. However, this same distance characteristic may be a challenge for periodic servicing mission. In this work, we introduce a new low-cost orbital transfer strategy that opportunistically combine chaotic and swing-by transfers to get a very efficient strategy that can be used for servicing mission on astronomical mission placed on Lagrangian points L4 or L5. This strategy is not only efficient with respect to thrust requirement, but also its time transfer is comparable to others known transfer techniques based on time optimization. Copyright ©2010 by the International Astronautical Federation. All rights reserved.

Peri-orbital bone dimensional analysis using computed tomography for placement of osseointegrated implants

Craniofacial osseointegrated implants enabled producing implant-retained facial prosthesis, namely the orbital prosthesis. Aim: To evaluate the length and width of the bone structure of the peri-orbital region and to present the method validation. Methods: Computed tomography scans of 30 dry human skulls were obtained in order to register linear length and width measurements of the periorbital region. Two examiners made the measurements twice with intervals of at least 7 days between them. Data were analyzed by descriptive statistics and the paired Student's t-test was used as inferential technique (SAS, α =0.05). Results: In most cases, the intra- and inter-examiner variations were not significant (p>0.05). Therefore, the method proposed was considered as precise and valid for the measurement of the peri-orbital region. The measured points correspond to the hours of a clock. The major lengths were observed at 1 h (18.32 mm) for the left peri-orbital bone and at 11h (19.28 mm) for the right peri-orbital bone, followed by the points situated at 2h (13.05 mm) and 12h (11.37 mm) for the left side and at 10 h (12.34 mm) and 12 h (11.56 mm) for the right side. It was verified that the three points with lowest values followed the same anatomical sequence in the supraorbital rim for the right and left orbits, showing compatibility with the insertion of the intraoral osseointegrated implants. The medial wall of both orbits did not present sufficient length to allow the insertion of intraoral or craniofacial implants. Conclusions: The largest width points were observed in the supraorbital rim and in the infralateral region of both orbits and those of smallest width were found in the supralateral region of both orbits.

Biocompatibility analysis of Bioglass® 45S5 and Biosilicate® implants in the rabbit eviscerated socket

Purpose: Bioactive glass and bioactive glass-ceramic cone implants were placed in the rabbit eviscerated socket to assess their biocompatibility. Methods: Fifty-one Norfolk albino rabbits underwent evisceration of the right eye followed by implantation of cones made from Bioglass® 45S5 (control group) and two types of bioactive glass-ceramic (Biosilicate®), a single- and a two-phase bioactive glass-ceramic implants into the scleral cavity. Postoperative reactions, animal behavior and socket conditions were monitored daily. Clinical exam, biochemical evaluations, and orbit computed tomographic scan were done at 7, 90, and 180 days post-procedure. After that, the animals were euthanized, and the orbital content was removed and prepared to light microscopy with morphometric evaluation and scanning electron microscopy examination. Statistical analysis was done by parametric and non-parametric analysis of variance, complemented by Dunn's and Tukey's tests (p<0.05). Results: All animals did not develop systemic toxicity throughout the experimental period and also did not have orbit infection, implant migration or extrusion. Morphological analysis demonstrated pseudocapsule around all implants. Bioglass® and single-phase Biosilicate® implants induced less inflammation and pseudocapsule formation than two-phase Biosilicate® cones. Seven days post-procedure, the inflammatory reaction was intense and gradually decreased throughout the experiment. Tissue reaction was least intense in animals receiving Bioglass® implants. Conclusions: We observe discrete differences among the studied materials, with best responses obtained with use of Bioglass® 45S5 and single-phase Biosilicate®. The authors agree these implants might be useful in the management of the anophthalmic socket. © 2012 Informa Healthcare USA, Inc.

The swing-by effect in the Vesta-Magnya case. Single and multiple encounters.

It was verified that the asteroid Magnya has some physical and chemical characteristics similar to the bodies from Vesta family. However, astronomical observations revealed that Magnya is distant from these bodies. In the present work, we assumed that Magnya originated from Vesta and we try to justify its current distant orbital location taking into account the effects of close encounters between Magnya and Vesta. The methodology adopted involved an analytical approach considering the technique of the gravity assisted maneuver, also known as swing-by. We found that the energy variation achieved through a single swing-by between Vesta and Magnya are very small when compared to the variation that would be required to change the orbit of Magnya. The effects of multiple close encounters were also considered and discussed. We concluded that the possibility of multiple encounters is limited, and therefore, that Magnya should suffer other perturbations (such as resonances, collisions or close encounters with other bodies, for instance) that would provide the supposed change in its orbit.

Spin stabilized satellite's attitude propagation with quaternions

This paper presents a study of a modeling scheme for the spin stabilized satellites attitude, entirely developed in terms of quaternion parametrization. The analysis includes numerical propagation of the rotational motion equation, considering the influence of the following torques: aerodynamic, gravity gradient, residual magnetic, eddy currents and the one due to the Lorentz force. Applications are developed considering the Brazilian Spin Stabilized Satellites SCD1 and SCD2, which are quite appropriated for verification and comparison of the theory with the real data generated and processed by the INPE's Satellite Control Center (SCC). The results show that for SCD1 and SCD2 the influence of the eddy current torque is bigger than the others ones, not only due to the orbit altitude, but also to other specific satellites characteristics. The influence of the torque due to Lorentz force is smaller than the others ones because of the dimension and the electrical charges of the SCD1 and SCD2. In all performed tests the errors remained within the dispersion range specified for the attitude determination system of INPE's SCC. The results show the feasibility of using the quaternion attitude parametrization for modeling the satellite dynamics of spin stabilized satellites.