Abstract: The formulation of kinematics and dynamics of multibody system basedon the fully Cartesian coordinates has an important advantage incomputational efficiency. In present paper the analytical expression oflinear and angular momentums of rigid body and multibody system in fullyCartesian coordinates and the coresponding generalized inertia matrix are given. The dynamics of a torque-free multibody system described by the fully Cartesian coordinates in the form of differential equations of first order is formulat...