Lagrange dynamics of lumped-mass multibody models of overhead cranes in 2D operational space

In this report the Lagrange dynamics of overhead cranes is analyzed, in the particular 2D (two-dimensional) operating space. Models can be classified according to different criteria: linear vs nonlinear, finite-dimensional vs infinite-dimensional (PDEs), control-design oriented vs numerical-simulation oriented, 2D operating space vs 3D operating space, etc. In this report we shall focus on 2D operational space models, and we shall provide a detailed study of a lumped-mass Lagrangian model of the cable. In spite of the fact that several toolboxes allow to derive automatically (or numerically) the dynamics of such multibody systems, it is of interest to obtain a deeper understanding of their structure and properties, to pave the way for control design and stability analysis