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Fig. 2.

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Topology of the Hamiltonian (Eq. (12)) on the representative RVφ plane. The continuous curves are the levels of the angular momentum Lz = R × Vφ, while the dashed curves are the energy levels, calculated with the fixed initial values pR = 0, z = 0 and Vz = 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 Lz-value due to conservation of the angular momentum, Lz. The conservation of the energy during the motion defines two turning points of each orbit, both lying at the intersections of the corresponding Lz- and energy levels. Top panel: the total energy (see Eq. (12)), in arbitrary units, calculated along the rotation curve, as a function of R.

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