Top-left panel: Toomre diagram for stars in LP sample. The vertical dashed line separates prograde from retrograde motions. Velocities are in units of km/s. The grey area separates stars with km s⁻¹ from stars with higher relative velocities with respect to the LSR. Top-right panel: distribution of the LP First stars in the L_z − L_perp plane. Angular momenta are in units of 100 kpc km s⁻¹. Middle-left panel: distribution of LP First stars in the E − L_z plane. The vertical dashed line separates prograde from retrograde motions. Angular momenta are in units of 100 kpc km s⁻¹, energies in units of 100 km² s⁻². Middle-right panel: distribution of LP First stars in the eccentricity-L_z plane. Bottom-left panel: distribution of stars in the z_max − R_max plane. The inset shows the whole distribution, over 60 kpc from the Galactic centre, while the main panel shows a zoom in the innermost 20 kpc. Filled symbols indicate stars with prograde orbits, empty symbols stars with retrograde orbits. Blue points show the comparison with the sample of stars analysed by Haywood et al. (2018). Units are in kpc. Bottom-right panel: normalised distribution of the arctan(z_max/R_max) for stars in the LP sample (black histogram), compared to stars studied by Haywood et al. (2018; blue histogram). In all panels, uncertainties have been estimated as described in Sect. 3.1.