A direct derivation of the equations of motion for 3D-flexible mechanical systems

Equations of motion for rigid bodies with the body-Þxed co-ordinate system placed at or away from the centre of mass are derived in a clear and direct way by making use of the two basic equations of mechanics (NewtonÕs second law and the corresponding law of angular momentum). The dynamic equations for ßexible mechanical systems are derived using the principle of virtual work, which introduces inertia in a straightforward manner, because this principle treats inertia as a force. The ßexible formulation is exempliÞed by the use of circular beam elements and some basic matrices are derived in a direct way using skew-symmetric matrices. The capabilities of the formulation are demonstrated through examples. Results are compared with and veriÞed by examples from the literature. Derivations throughout the paper are simpliÞed by means of skew-symmetric matrices