  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 3D 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 $L_z$ and orbital precession rate
$\Omega_\mathrm{pr}$ (normal orbital mode) change to synchronous (abnormal
mode). The transition to the abnormal mode occurs when $\Omega_\mathrm{pr}$
reaches the angular velocity of the pattern $\Omega_\mathrm{p}$, after which
the orbit becomes stuck in the bar trap. All this happens against the
background of secular changes in actions ($L_z$ decreases, $J_\mathrm{R}$ and
$J_z$ increase). At the same time, corotation particles near two stable
Lagrange points are also subject to secular changes in their actions. They
increase $L_z$ and drift to the periphery, shifting corotation outwards. We
also show that a change in the orbital mode from normal to abnormal and the
trapping of orbits in a bar is possible only when the bar speed decreases with
time, regardless of what is causing the bar to slow down. Our findings clarify
and expand the picture of bar formation and evolution in numerical models.
