The Melnikov Analysis of the Pitch Dynamics of a Gravity Gradient Satellite

The pitch motion of a generic gravity gradient satellite is investigated in terms of chaos. The Melnikov method is used for detecting the onset of chaotic behavior of the pitch motion of a gravity gradient satellite. The Melnikov method determines the distance between stable and unstable manifolds of a perturbed system. When stable and unstable manifolds transverse on the Poincare section, the resulting motion can be chaotic. The Melnikov analysis indicates that the pitch dynamics of a generic gravity gradient satellite can be chaotic when the orbit eccentricity is small.