Nl. Pedersen et Ml. Pedersen, A DIRECT DERIVATION OF THE EQUATIONS OF MOTION FOR 3D-FLEXIBLE MECHANICAL SYSTEMS, International journal for numerical methods in engineering, 41(4), 1998, pp. 697-719
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.