Evolution of Saturn’s spin axis and Titan’s orbit while following the centre of the secular spin–orbit resonance with s₈. We use blue for Saturn’s spin axis and red for Titan’s orbit. Each panel is described directly on the graph when the legend is not self-explanatory. In the right column, time is shown both in normalised units (left vertical axis) and in physical units (right vertical axis). The conversion factors are given in Table 1. All curves are obtained through the analytical formulas described in the text, assuming that Saturn closely oscillates near Cassini state 2 and Titan closely oscillates near Laplace state 1. In the top left panel, the green curve shows the location of the resonance centre according to the formula used by Saillenfest et al. (2021b) valid for a close satellite. In the bottom right panel, the black curve in the unstable region corresponds to the period needed for the eccentricity to be multiplied by exp (2π) ≈ 535.