A skew-symmetric property of rigid-body systems

Abstract

The configuration space for the attitude of a vehicle can be modeled as SO(3), namely the rotation matrix group. This work investigates the globally valid dynamics of natural Lagrangian systems and gyroscopic systems with configuration space including SO(3). The dynamics is derived by using the global representations of jet bundles of SO(3). A skew-symmetric property associated with the systems can be then established. Such property can be used in many applications such as the adaptive controller design. © 1998 Elsevier Science B.V. All rights reserved.