We have translated the results of N-body simulations of one barred model into the language of action variables and frequencies. Using this language, we analysed the behaviour of all orbits in the model on a large time-scale at the stage of a mature bar. We show that the orbits join the bar while preserving their adiabatic invariant, which takes into account the three-dimensional structure of the orbits. This allows us to apply the concept of the Lynden-Bell derivative for each of these orbits and trace how the sign of the derivative changes; i.e. how asynchronous changes in angular momentum Lz and orbital precession rate.