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- Dynamics of a gyrostat satellite with the vector of gyrostatic moment tangent to the orbital planePublication . Morais, Renato; Santos, Luis; Silva, André; Melício, RuiIn this paper, a gyrostat satellite in a circular orbit with its gyrostatic moment tangent to the orbital plane and collinear with the orbital speed is studied regarding its equilibria, bifurcation of equilibria, and asymptotic stability conditions. In the general case, where any gyrostat angular momentum is aligned with any of the orbital coordinate frames, interesting results arose regarding its equilibria bifurcation regarding conditions near to the ones presented in this paper, namely equilibria regions outside their main regions near to the orbital plane tangent. For equilibria and bifurcation of equilibria, a symbolic-numerical method is used to obtain the polynomial equations in function of non-dimensional parameters whose roots are equivalent to the number of equilibria positions. For the asymptotic stability, the results are tested using the Lyapunov stability theory scheme.
- Gyrostat Dynamics on a Circular Orbit: General Case of Equilibria Bifurcation and Analytical ExpressionsPublication . Santos, Luís; Melício, Rui; Silva, A. R. R.This paper is on the study of the Dynamics of a Gyrostat Satellite on a Circular Orbit, and the achievement of the analytical expressions which describes the bifurcation of equilibria. The attitude control of modern spacecraft's is essential to fulfil its missions. Every time that is necessary to point a camera or a scientific instrument the space platform must be perfectly balanced and stabilized. When a space platform loses its ability to be balanced and stabilized, which might be due to several factors, loses also its ability to carry out its mission. One approach to achieve such conditions is using Gyrostat configuration.
- Short-Term Consequences of Asteroid Impacts into the Ocean: A Portuguese Case StudyPublication . Morais, Renato; Santos, Luís; Silva, A. R. R.; Melício, RuiAsteroid impacts are a proven global threat, meaning that any location on Earth might be a subject to their consequences. Such collisions are not likely in any person’s lifetime, but their aftermath could be catastrophic. As Earth’s surface is mostly water, a water impact is more probable than a ground impact, and tsunami waves could pose a significant threat. This study expands the knowledge about asteroid impacts in the ocean and their regional environmental consequences. Three asteroids were assumed to impact the Earth: (1) the Apophis asteroid, a 370 m wide asteroid, (2) a 204 m in diameter asteroid representative of the average impactor on the near-Earth objects, and (3) a 5 km in diameter asteroid. We evaluated the consequences of all impacts for a specific case study, where the chosen impact location was the midpoint between Portugal’s mainland, Azores, and Madeira Islands. The cratering process, generated seismic shaking, overpressure, ejected material, induced thermal radiation, and tsunami waves were assessed, along with the global effects. The overpressure mainly causes structural damage. The thermal radiation can be devastating but has a short reach. The tsunami is undoubtedly the most far-reaching and threatening effect of an asteroid impact in the ocean.
- Dynamics of a gyrostat satellite subjected to the action of gravity moment. Equilibrium attitudes and their stabilityPublication . Gutnik, S.A.; Santos, Luís; Sarychev, V. A.; Silva, A. R. R.We study the dynamics of the rotational motion of a gyrostat satellite moving in the central Newtonian force field along a circular orbit. We propose a method for determining the equilibrium attitudes (equilibrium orientations) of a gyrostat satellite in the orbital coordinate system for given values of the gyrostatic moment vector and principal central moments of inertia, and obtain their existence conditions. For each equilibrium orientation, sufficient conditions for stability are obtained using a generalized energy integral such as a Lyapunov function. We conduct a detailed numerical analysis of domains where the stability conditions for equilibrium attitudes are satisfied depending on four dimensionless parameters of the problem. It is shown that the number of equilibrium attitudes of a gyrostat satellite for which the sufficient conditions of stability are satisfied in the general case varies from four to two with an increase in the magnitude of a gyrostatic moment. The results obtained in this paper can be used for constructing gravitational systems of control over the orientation of the Earth’s artificial satellites.
- Gyrostat dynamics on a circular orbitPublication . Santos, Luís Filipe Ferreira Marques; Silva, André Resende Rodrigues daThis work deals with a general gyrostat moving along a circular orbit in a central Newtonian force field. The main purpose is to determine all equilibria positions for our spacecraft in the case when internal angular momentum of the gyrostat satellite is collinear to its principal axis of inertia, when the gyrostatic moment vector lies in one of the satellite’s principal central plane of inertia and for a general position where the gyrostatic moment doesn’t coincide with any of the principal axis of inertia.
- Hypothetical Apophis deep ocean impact - Energy analysisPublication . Morais, Renato; Santos, Luís; Silva, André; Melício, RuiThis paper models a hypothetical Apophis asteroid impact on an chosen deep ocean point on the globe. To assess the potential vulnerabilities of an exposed coast population, the impact effects were assessed as a function of the distance to the asteroid's impact point as well as altitude for the tsunami case. All the tools and models used are valid and can be implemented for any other point on the Earth's surface. The impact modelling includes the analysis of cratering formation, generated earthquake, overpressure, ejected material, generated thermal radiation and tsunami, as well as the global geophysical effects of the impact. The vulnerability models entail best, expected, and worst case scenarios, which allows a reasonable range of results. As the impact occurs in the ocean, and if its a great distance away from populated areas, the population is safeguarded from most of the impact effects. The tsunami is undoubtedly the most far-reaching and threatening impact effect from an asteroid impact on the ocean.
- Dynamics of gyrostat satellite subject to gravitational torque: Stability analysisPublication . Sarychev, Vasili; Gutnik, S. A.; Silva, André; Santos, LuísDynamics of gyrostat satellite moving along a circular orbit in the central Newtonian gravitational field is investigated. A symbolic-numerical method for determining of all equilibrium orientations of gyrostat satellite in the orbital coordinate system with given gyrostatic torque and given principal central moments of inertia is proposed. For each equilibrium orientation sufficient conditions of stability are obtained as a result of analysis of generalized energy integral used as Lyapunov’ function. Investigation of domains where stability conditions take place is provided in detail depending on four dimensionless parameters of the problem. It is shown that the number of stable equilibria of the gyrostat satellite in general case changes from 8 to 4 with the increasing the absolute value of gyrostatic torque.
- Dynamics of gyrostat satellite subject to gravitational torque: Investigation of equilibriaPublication . Sarychev, Vasili; Gutnik, S.A.; Silva, André; Santos, LuísDynamics of gyrostat satellite moving along a circular orbit in the central Newtonian gravitational field is investigated. A symbolic-numerical method for determining all equilibrium orientations of gyrostat satellite in the orbital coordinate system with given gyrostatic torque and given principal central moments of inertia is proposed. Conditions of equilibriums existence are obtained depending on four dimensionless parameters of the system. All bifurcational values of parameters at which there is a change of numbers of equilibrium orientations are determined. Evolution of domains in the space of parameters which correspond to various numbers of equilibria are carried out in detail. Relationship with axisymmetrical cases of satellite gyrostat is considered. It is shown that the number of equilibria of the gyrostat satellite in general case not be less than 8 and not more than 24.
- Gyrostat dynamics on a circular orbitPublication . Santos, Luís Filipe Ferreira Marques; Silva, André Resende Rodrigues da; Sarychev, Vasili A.The attitude control of a modern satellite is a crucial condition for its operation. In this work, is investigated the dynamics of an asymmetrical inertial distribution gyrostat satellite, subjected to gravitational torque, moving along a circular orbit in a central Newtonian gravitational field. To solve the problem it is proposed a symbolic-numerical method for determining all equilibrium orientations of an asymmetrical gyrostat satellite in the orbital coordinate system with a given gyrostatic torque and given principal central moments of inertia. The conditions of equilibria are obtained depending on four dimensionless parameters of the system. The evolution of the domains in the study of equilibria and stability is carried out in great detail. All bifurcation values of parameters at which there is a change of numbers of equilibrium orientations are determined with great accuracy. For each equilibrium orientation the sufficient conditions of stability are obtained as a result of analysis of the generalized integral of energy used as a Lyapunov’s function. It is shown that the number of equilibria of a gyrostat satellite in the general case must be between 8 and 24, and that the number of stable equilibria changes from 4 to 2.
- Asteroid Impacts on the Ocean and Its Short-term Consequences: a Portuguese Case StudyPublication . Morais, Renato; Santos, Luís; Silva, A. R. R.; Melício, RuiAny location on Earth might be considered a subject to an asteroid impact because, as previous studies show, they are a proven global threat. the consequences of a collision could be catastrophic, even though such events are rare to occur in a person’s lifetime. Tsunami waves can constitute the greatest threat as the Earth’s surface is mostly water, making the probability of a water impact greater than a ground impact. This work expands the knowledge about asteroid impacts on the ocean and their short-term regional consequences. Three asteroids were assumed to impact the Earth: (1) the 2015 JJ asteroid with a 130 m diameter, (2) the 2020 FA5 asteroid with a 210 m diameter, and (3) the Apophis asteroid, a 370 m wide asteroid. We evaluated the consequences of all impacts, at a 45 degree angle, for a specific case study, where the chosen impact location was the midpoint between Portugal’s mainland, Azores, and Madeira Islands. The cratering process, overpressure, induced thermal radiation, and tsunami waves were assessed, along with the global effects. The overpressure mainly causes structural damage. The thermal radiation has too short a range to reach the studied localities. The tsunami is undoubtedly the most far-reaching and threatening effect of an asteroid impact in the ocean.