Add to ORKGInternational audienceThis article presents a unified dynamic modeling approach of continuum robots. The robot is modeled as a geometrically exact beam continuously actuated through an active strain law. Once included into the geometric mechanics of locomotion, the approach applies to any hyper-redundant or continuous robot devoted to manipulation and/or locomotion. Furthermore, exploiting the nature of the resulting models as being a continuous version of the Newton-Euler models of discrete robots, an algorithm is proposed which is capable of computing the internal control torques (and/or forces) as well as the rigid overall motions of the locomotor robot. The efficiency of the approach is finally illustrated through many examples directly...