Six methods to model a flexible beam rotating in the vertical plane

This paper presents six methods to model a flexible beam rotating in the vertical plane. The first three methods, Hamilton´s principle, Lagrange´s equations for quasi-coordinates and Newton-Euler equations, give a continuous model. The last three methods, Lagrange´s equations, Jourdain´s principle and Newton-Euler equations, give a discrete model. The paper discusses how the different methods apply. It also shows how to derive the discrete model directly from the continuous one. The main conclusion of the paper is that if the foreshortening of the flexible link is neglected, then starting from the same assumptions, different methods give different models.