An Observer Design and Separation Principle for the Motion of the n-dimensional Rigid Body

In this note it is shown how the n-dimensional rigid body equation naturally leads to Hamilton's canonical equation and how this may be used for controller and observer designs by using the geometry of mechanical systems on manifolds avoiding the parameterization of Lie group SO(n). Based on this approach, it is possible to focus on the intrinsic property of the system and to show closed-loop stability, a separation principle, which has been conjectured but not yet been shown.