x₂ family of orbits for the model of Eq. (8) for (a) a pattern speed Ω_sp = 15 km s⁻¹ kpc⁻¹ and density of the spiral potential ρ₀ = 5 × 10⁷ M_⊙ kpc⁻³ in (a), ρ₀ = 15 × 10⁷ M_⊙ kpc⁻³ in (b) and ρ₀ = 30 × 10⁷ M_⊙ kpc⁻³ in (c). In all three cases, these elliptical orbits do not support the spiral wave derived from the galactic potential, and their main axes are perpendicular to the main axes of the x₁ family.