  Derivatives of equations of motion describing the rigid body dynamics are
becoming increasingly relevant for the robotics community and find many
applications in design and control of robotic systems. Controlling robots, and
multibody systems comprising elastic components in particular, not only
requires smooth trajectories but also the time derivatives of the control
forces/torques, hence of the equations of motion (EOM). This paper presents
novel nth order time derivatives of the EOM in both closed and recursive forms.
While the former provides a direct insight into the structure of these
derivatives,the latter leads to their highly efficient implementation for large
degree of freedom robotic system.
