Coplanar equilibrium solutions and examples of orbital evolution using the full-space (nonlinear) disk gravity model (a) and the approximate linear model (b). The upper panels of (a) and (b) show equilibrium solutions as a function of ϵ_⋆d (or ${ϵ}_{\star \mathrm{d}}^{\mathrm{\prime }}$) for ψ_⋆0 = 70°. In (a), the coplanar equilibria (P₂, P₃, P₄, and P₅) and bifurcations (B₁ and B₂) are denoted. The lower panels of (a) and (b) show the evolution of the stellar obliquity through numerical integrations of corresponding secular equations. The dashed curves in the two panels represent the evolution of the equilibria.