Periodic approximation of spacecraft Foton-12 attitude motion

We constructed the real uncontrolled attitude motion of Photon-12 spacecraft (was in orbit from 09.09 to 24.09.1999) by periodic solutions of a conservative system of differential equations. For this purpose we repeated processing of the magnetic measurements made on board the spacecraft. At repeated processing the simplified mathematical model of attitude motion was used. The actual satellite orbit (apogee altitude 380 km, perigee altitude 220 km) was replaced by a circular one, the formula of aerodynamic torque acting on the spacecraft was simplified. The system of differential equations underlying the new model is autonomous and provides a fairly accurate reconstruction of the spacecraft motion by magnetic measurements. On some segments of the motion, the conjunction of which covers about a quarter of the flight (3 days), this system can be reduced to a conservative one. Such a reduction leads to a more specific set of its solutions, suitable for an approximate description of the real movement of the spacecraft. We used for this purpose periodic solutions, continued numerically from Lyapunov's periodic solutions.