Study of Stability of Rotational Motion of Spacecraft with Canonical Variables

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.

Tidal Variations of the Earth Rotation

The equations for the rotation of a weakly deformable celestial body in non canonical Andoyer variables have been used to study the perturbation of Earth rotation due to tidal deformation raised by the Moon and Sun. A theory of the perturbed rotational motion of an isolated weakly deformable body in Andoyer variables and in components of the angular velocity has been developed. Mantle tidal deformations due to lunar and solar influences were analytically described and taken into account. Perturbations of the first order in the Earth’s polar motion were determined.