Example of a long-term evolution of Eulalia’s obliquity ε. Here we assumed pole P1 orientation for the initial data and numerically integrated orbit and spin evolution for the next 10 Myr interval of time. The rotation period was assumed constant, and equal to its current value of ≃29 h, and the dynamical flattening set to Δ = 0.25. Bottom panel: obliquity ε (right ordinate) and/or cosε (left ordinate) vs time in the simulation. The obliquity exhibits large oscillations between ~45° and ~85° in two distinct regimes due to overlap of Cassini resonances related to the s and s₆ orbital frequencies. Middle and top panels: Phase angle of the Cassini resonance of the s₆ frequency (middle) and the s frequency (top). Intermittent periods of libration correlate with the range of the obliquity oscillations at the bottom panel.