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Gyrostat dynamics on a circular orbit
Publication . 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.
2015Doctoral thesis Open access Show more