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Abstract
This work aims to analyze the stability of the rotational motion of artificial satellites in circular orbit with the influence of gravity gradient torque, using the Andoyer variables. The used method in this paper to analyze stability is the Kovalev‐Savchenko theorem. This method requires the reduction of the Hamiltonian in its normal form up to fourth order by means of canonical transformations around equilibrium points. The coefficients of the normal Hamiltonian are indispensable in the study of nonlinear stability of its equilibrium points according to the three established conditions in the theorem. Some physical and orbital data of real satellites were used in the numerical simulations. In comparison with previous work, the results show a greater number of equilibrium points and an optimization in the algorithm to determine the normal form and stability analysis. The results of this paper can directly contribute in maintaining the attitude of artificial satellites.
Highlights
Stability analysis of the rotational motion of a satellite taking into account the influence of external torques is very important in maintaining the attitude to ensure the success of a space mission.Recently, some studies on the subject have been developed, and they motivated the development of this paper
This work aims to analyze the stability of the rotational motion of artificial satellites in circular orbit with the influence of gravity gradient torque, using the Andoyer variables
In comparison with previous work, the results show a greater number of equilibrium points and an optimization in the algorithm to determine the normal form and stability analysis
Summary
Stability analysis of the rotational motion of a satellite taking into account the influence of external torques is very important in maintaining the attitude to ensure the success of a space mission.Recently, some studies on the subject have been developed, and they motivated the development of this paper. Stability analysis of the rotational motion of a satellite taking into account the influence of external torques is very important in maintaining the attitude to ensure the success of a space mission. In 1, 2 is presented a study on the stability of the rotational motion of artificial satellites in an elliptic orbit, considering disturbance due to gravity. Mathematical Problems in Engineering gradient torque, using canonical formulations and the Andoyer canonical variables. These studies use the procedure presented in 3 to determine a normal form of the Hamiltonian up to 4th order. The most important role of this work is the results obtained analytically for the generating function of 3rd order, necessary for determining the coefficients of the normal Hamiltonian of 4th order
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