The problem of mathematical modelling and indication of properties of a DIP has been investigated in this paper. The aim of this work is to aggregate the knowledge on a DIP modelling using the Euler-Lagrange formalism in the presence of external forces and friction. To indicate the main properties important for simulation, model parameters identification and control system synthesis, analytical and numerical tools have been used. The investigated properties include stability of equilibrium points, a chaos of dynamics and non-minimum phase behaviour around an upper position. The presented results refer to the model of a physical (constructed) DIP system.