Numerical and analytical approach for the spin-stabilized satellite attitude propagation

This paper presents the comparison between the numerical and analytical results of a spacecraft attitude propagation for a spin-stabilized satellite. Some external torques are introduced in the equations of the motion and the comparisons are done considering that these torques are acting together, which are: gravity gradient, aerodynamic, solar radiation, magnetic residual and eddy current. In the numerical approach it is used the quaternion to represent the attitude. This numerical approach can be applied for any kind of satellite. The analytical approach is applied directly for a spin-stabilized satellite and the equations of motion are described in terms of the spin velocity, spin axis right ascension and declination angles. An analytical solution of these equations is presented and valid for one orbit period. Applications are developed considering the Brazilian spin-stabilized satellites SCD1 and SCD2. The comparisons are important to validate some simplifications that are required in the analytical approach. The results show that the average components of the external torque are sufficient to observe the main influence of the considered torques.