We present a multi-contact motion planning method that generates dynamic joint trajectories for multi-body robots that satisfy a set of continuous constraints. We highlight two variants when it comes to generate a single-contact or a multi-contact motion: the presence of the continuous equality geometrical constraints and of the contact forces. In this work, we compute the free-flyer trajectory and the contact forces from the joint trajectories provided by the optimization process. We assess our method on three dynamical multi-contact motions with 2D models. The comparison with intuitive adaptations of the single-contact motion planning methods shows the effectiveness of our method.