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- 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.
- 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.