The intention of the paper is to review and compare existing formulations for flexible beams under large overall motion with reference to both the inertial frame approach and to the floating frame approach. These two choices of writing the equations of motion are presented with relevance to the dynamics of flexible bodies in planar motion. For the inertial frame approach, non-linear partial differential equations based on two finite strain rod models are reviewed. For the floating frame approach, linear and non-linear partial differential equations based on the finite strain rod model, the Euler-Bernoulli beam model with the von Karman geometric constraint, the consistent second order theory, the Green-Lagrange theory, and the Kane-Ryan-Banerjee approach are derived and compared. In Part II the numerical simulation of the theoretical developments is presented, which includes the numerical comparison of the various non-linear formulations.