Dynamic decomposition of the bar (ILR) at the beginning of buckling (t = 160, two top row) and at the peak of buckling (t = 180, two bottom row). For each time moment, the five leftmost snapshots on the xy-plane, covering [ − 2.5, 2.5]×[−2.5, 2.5], and on the xz-plane, covering [ − 2.5, 2.5]×[−1.5, 1.5], are shown. From left to right: All bar orbits (ILR); orbits with increasing resonant angle, θ_res = θ_z − θ_R (vCIR+); orbits in the vILR (BAN); orbits passing through it (vPAS); and orbits with decreasing θ_res (vCIR−). The next five snapshots show the same orbits on the xz-plane, but separated into “up” (near θ_res = 0) and “down” (near θ_res = π) types, and into secular J_z < 0.02 (very flat) and J_z > 0.02 (thick) for BAN orbits. For more information on the classification of these types, see Sect. 3 and Appendix A.