A DIRECT DERIVATION OF THE EQUATIONS OF MOTION FOR 3D-FLEXIBLE MECHANICAL SYSTEMS

Equations of motion for rigid bodies with the body-fixed co-ordinate s ystem 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 (Newton's second law and the corresponding law of angular momentum). T he dynamic equations for flexible mechanical systems are derived using the principle of virtual work, which introduces inertia in a straight forward manner, because this principle treats inertia as a force. The flexible formulation is exemplified by the use of circular beam elemen ts and some basic matrices are derived in a direct way using skew-symm etric matrices. The capabilities of the formulation are demonstrated t hrough examples. Results are compared with and verified by examples fr om the literature. Derivations throughout the paper are simplified by means of skew-symmetric matrices. (C) 1998 John Wiley & Sons, Ltd.