Non-linear dynamics of elastic curvilinear systems. A new coordinateless approach

Using the theory of Lie groups, a mechanical model is developed and the equations of motion are written in coordinateless form for an arbitrary curvilinear model of an elastic system with dimension no higher than three, starting from the unique hypothesis of a continuous distribution of rigid bodies, called sections. The proposed method is illustrated using examples of the automatic derivation of the corresponding scalar equations, by means of which one can describe all possible models of such systems as beams, cables, strings, etc.