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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.
- 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.