Continuous Newton-Euler Algorithms for Geometrically Exact Flexible Beams

A Newton-Euler formalism is derived for geometrically exact Cosserat beam theory in a purely deductive manner, thanks to an analogy with optimal control theory. The method relies upon a joint use of Gauss least constraint principle, Appell´s equations and optimal control theory, that was used in a previous work for the classical case of discrete Newton-Euler backward and forward recursions for multibody systems. Motivating applications are hyper-redundant manipulators or biomimetic robots such as eel-robots, undergoing large displacements