The goal of the present paper is to study close approaches of a cloud of particles with an oblate planet, which means that there is a J 2 term in the gravitational potential of the planet. This cloud of particles is assumed to be created during the passage of a spacecraft by the periapsis of its orbit, by an explosion or any other disruptive event. The system is formed by two large bodies (Sun and planet), assumed to be in circular orbits around the center of mass of the system, and the cloud of particles. The particles that belong to the cloud make a close approach to the flat planet and then they are dispersed by the gravitational force of the planet. The motion is governed by the equations of motion given by the planar restricted circular three-body problem plus the effects of the oblateness of the planet. Jupiter is used for numerical simulations. The results show the differences between the behavior of the cloud after the passage, considering or not the effects of the oblateness of the planet. The results show that the oblateness of the planet is equivalent to an increase in the mass of the planet.
Based on the Theory of Neuronal Group Selection (TNGS), proposed by Edelman, a network composed of one hundred Izhikevich spiking neurons is analyzed. In this study, a genetic algorithm is used to estimate the Izhikevich neuron model parameters in order to enable the self-organization of a neural network into a cluster of tightly coupled neural cells which fire and oscillate in synchrony at a predefined frequency.
The idea of the present paper is to study orbital transfers for a spacecraft from the Lagrangian points in the Earth-Moon system to the Earth, as well as to the other Lagrangian points. The model used is the restricted three-body problem with the addition of the effects of the radiation pressure in the trajectory of the spacecraft. The basic maneuver is a bi-impulsive transfers under the dynamics explained before. The results show that the radiation pressure has an influence in the process, although not very large. After that we made some simulations for similar maneuvers in a double asteroid system, where the gravitational forces are smaller and the radiation pressure gives important contributions to the motion of the spacecraft. It is possible to find solutions with smaller fuel consumption when considering the solar radiation pressure, in both cases, but with important reductions in the magnitude of the impulses required for the asteroid system. It is important always to take into account that the idea presented here is not to use the radiation pressure as a control, but just to measure its effects when performing the bi-impulsive transfer.
Abstract. There are many applications of the close approach maneuvers in astronautics, and several missions used this technique in the last decades. In the present work, those close approach maneuvers are revisited, but now considering that the spacecraft passes around an oblate planet. This fact changes the distribution of mass of the planet, increasing the mass in the region of the equator, so increasing the gravitational forces in the equatorial plane. Since the present study is limited to planar trajectories, there is an increase in the variation of energy given by the maneuver. The planet Jupiter is used as the body for the close approach, but the value of J2 is varied in a large range to simulate situations of other celestial bodies that have larger oblateness, but the same mass ratio. This is particularly true in recent discovered exoplanets, and this first study can help the study of the dynamics around those bodies. IntroductionSeveral papers in the literature describe the close approach maneuvers, like the ones shown in references [1] to [20]. Using the model given by the "patched conics" to explain the close approach maneuvers, it is assumed that the mission can be divided in three stages, all of them studied under Keplerian motion. It is also considered that the system consists of three bodies: M 1 , a massive body in the center of the Cartesian system; M 2 , a smaller body in a Keplerian orbit around M 1 ; and M 3 , a spacecraft that is traveling in an orbit around M 1 when it passes close to M 2 . This passage changes the orbit of M 3 , which leads to a variation of eccentricity, semi-major axis, velocity, energy and angular momentum of M 3 . This phenomenon is also called a swing-by maneuver. The advantages of this maneuver are the savings of time and fuel for a particular mission. According to these assumptions, the orbits of M 1 and M 2 remain unchanged. For the motion of the spacecraft, the model of two bodies is used in the initial phase, for the spacecraft-central body system. In the second stage, it is assumed that the spacecraft passes through the secondary body in an open trajectory. The third step is again assumed to be a system formed by two bodies, spacecraft-central body. The goal of this maneuver is to modify the Keplerian trajectories spacecraft-central body from the first to the third stage. Figure 1 illustrates this sequence. In this figure, A and B are the initial and final points of the trajectory during the close approach, is the angle of curvature of the spacecraft, is the angle between the periapsis line and the line connecting M 1 and M 2 , V 2 is the velocity of M 2 with respect to M 1 , and are the velocities of M 3 with respect to M 2 , when approaching and leaving M 2 , respectively, and rp is the periapsis distance of the close approach.
The present paper studies the effects of the radiation pressure in the trajectories of a spacecraft in transfers between the collinear Lagrange points of a double asteroid system. The system considered is this paper is formed by the double asteroid 1996FG 3 and the maneuvers are always assumed to be bi-impulsive. In a system formed by asteroids, the solar radiation pressure has a significant influence in the transfers paths. This occurs because the gravitational forces in these systems are smaller if compared with systems formed by larger bodies. Solutions with lower and higher fuel consumption can be found by adding the solar radiation pressure. The radiation pressure was not used as a control but its effects over the transfers were measured. For a small system of primaries such as an asteroid system, it is very important to take into account this force to make sure that the spacecraft will reach the desired point.
Inspired by the Theory of Neuronal Group Selection (TNGS), we have carried out synthesis of frequency generator via spiking neurons network through genetic algorithm. The TNGS sets that a neuronal group is the most basic unit in the cortical area and are generated by synapses of localized neural cells in the cortical area of the brain firing and oscillating in synchrony at a predefined frequency. Each one of these clusters (Neuronal Groups) is a set of localized, tightly coupled neurons developed in the embryo. According to this proposal, this paper describes a method of tuning the parameters of the Izhikevich spiking neuron model. Computational experiments consisting of a network with all neurons of the same type and a network with different neurons were conducted. A genetic algorithm was used to tune the parameters in these two different cases.The results were compared in order to find the best way to create a frequency generator of spiking neurons network.
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