Example of two orbits (red and blue) of disc stars in a barred potential in inertial (left) and rotating with the bar (right) reference frames. In the bottom panels, the orbits are colour-coded to indicate the progression of time. The ovals in the figure represent the bar orientation, with three different configurations colour-coded to denote changes in its orientation over time in the inertial frame. Notably, the orientation of the bar varies with time in the inertial reference frame while, by definition, it remains fixed in the rotating frame. Therefore, the orbits in the rotating frame allow us to exclude the time dependence of particle positions along the orbits and prevent phase-mixing, enabling us to use them in the orbit superposition approach.