Topology on representative angular planes. The eccentricities of the symmetric ACR are (e₁, e₂, e₃) = (0.00458, 0.00938, 0.00564). (a) Hamiltonian level curves on (θ₁₂, Δϖ₁₂) plane with (θ₂₃, Δϖ₂₃) fixed to (π, π), the saddle-like point at (θ₁₂, Δϖ₁₂) = (π, 0) is marked by a red cross. (b) Topology on (θ₂₃, Δϖ₂₃) plane with (θ₁₂, Δϖ₁₂) fixed to (π, 0). The node-like point at (θ₂₃, Δϖ₂₃) = (π, π) is marked by a red dot. In addition, the stable symmetric configuration (θ₁₂, Δϖ₁₂, θ₂₃, Δϖ₂₃) = (0, π, 0, π) is shown as blue dots.