Differential invariants of curves in Galilean geometry

Let Γn be an n-dimensional Galilean space over the field ℝ of real numbers, let Γ(n, ℝ) be the Galilean group of linear transformations in Γn and let ℝn ⨞Γ(n, ℝ) be the semidirect product of the groups ℝn and Γ(n, ℝ). We introduce the special invariant parametrization for curves α ⊂ Γ(n, ℝ), and using this parametrization we obtain criterion for the G-equivalence of curves α and β (i.e. β = g(α) for some g ∈ G) with respect to the action of groups Γ(n, ℝ) and ℝn ⨞Γ(n, ℝ).