Some models for the description of the attitude dynamics

The study of rotational dynamics is of seminal importance for the descrip- tion of the motion of natural and artificial bodies. In this work with are mainly interested to the attitude of spacecraft, possibly including dissipative effects, which must be ac- curately accounted during mission design as they might drastically change the attitude and lead to instability and mission failure. We review some models of rotational dynamics. The first one is the spin–orbit prob- lem describing the motion of a satellite rotating around an internal spin–axis and moving on a Keplerian orbit around a planet. An interesting application of KAM theory to this model will be shortly reviewed ([6]). We will also discuss dissipative tidal effects, which might act on the system. The second model is the so–called pitch-yaw-roll problem. In particular, we consider the pitch model, in which the yaw and roll angles are constantly zero; we shall also assume that one of the moments of inertia depends on time and that the atmospheric drag acts on the system. Following [21], we provide an interesting application of Melnikov’s method to establish the onset of chaos by evaluating the exis- tence of heteroclinic intersections. The third model concerns the sloshing effect acting within a spacecraft; assuming a linear motion of the fluid in the spacecraft, this prob- lem will be mathematically described using an equivalent mechanical model by suitably combining springs, pendulums and dampers ([33]). The last problem describes the ef- fects of a variable mass (e.g., due to fuel consumption) on the attitude of the spacecraft. This model admits an explicit solution in the case in which the container has cylindrical shape .