Topology of the Hamiltonian (Eq. (12)) on the representative R–V_φ plane. The continuous curves are the levels of the angular momentum L_z = R × V_φ, while the dashed curves are the energy levels, calculated with the fixed initial values p_R = 0, z = 0 and V_z = 20 km s⁻¹. The rotation curve is shown by red dots. The projections of the three 3D orbits on the plane are: the Sun’s orbit (cyan dots), one orbit starting at configuration 1, and another at configuration 2 (black dots). The motion always occurs along a fixed L_z-value due to conservation of the angular momentum, L_z. The conservation of the energy during the motion defines two turning points of each orbit, both lying at the intersections of the corresponding L_z- and energy levels. Top panel: the total energy (see Eq. (12)), in arbitrary units, calculated along the rotation curve, as a function of R.