Δ y$_{2}$ | $^{y}$∈ Γ$_{1}$ = − y$_{2}$ − R$_{1}$y 2 $_{2}$, Δ y$_{2}$ | $^{y}$∈ Γ$_{2}$ = − (1 + R$_{2}$ ) y$_{2}$, (3.14b) with the domain D = R $^{2}$, R$_{1}$ = exp( − 0 . 0005 π ) and R$_{2}$ = 0 . 9 . In the paper [16], it is stated that the coefficient of restitution for low velocity impact still remains as an open problem. In the study [4], by considering Kelvin-Voigt model for the elastic impact, we derived quadratic terms of the velocity in the impact law. This arguments make the quadratic term for the impulse equation (3.14b) reasonable. Let us describe the set of discontinuity curves by Γ = Γ$_{1}$ ∪ Γ$_{2}$ . The components Γ$_{1}$ and Γ$_{2}$ are intervals of the vertical lines y$_{1}$ = exp(0 . 00025 π ) and y$_{1}$ = 0 , respectively and they will be precised next. Fix a point P = (0 , ¯ y$_{2}$ ) ∈ D, with ¯ y$_{2}$ > 1 . Let y ( t, 0 , P ) be a solution of (3.14a) and it meets with the vertical line x$_{1}$ = exp(0 . 00025 π ) , x$_{2}$ > 0 at the point P$_{2}$ = (exp(0 . 00025 π ) , y$_{2}$ ( θ$_{1}$, 0 , P )) , where θ$_{1}$ is the meeting moment with the line. Consider the point Q$_{2}$ = (exp(0 . 00025 π ) , − R$_{1}$y$_{2}$ ( θ$_{1}$, 0 , P$_{2}$ ) $^{2}$) and denote Q$_{1}$ = (0 , y$_{2}$ ( θ$_{2}$, 0 , Q$_{2}$ )) , where θ$_{2}$ is the moment of meeting of the solution y ( t, 0 , Q$_{2}$ ) with the vertical line x$_{1}$ = 0 , x$_{2}$ < 0 . We shall need also the point P$_{1}$ = (0 , − R$_{2}$y$_{2}$ ( θ$_{2}$, 0 , Q$_{2}$ )) . Finally, we obtain the region G in yellow and blue between the vertical lines and graphs of the solutions in Figure 1. The region G contains discontinuous trajectories and outside of this region all trajectories are continuous. Moreover, both region G and its complement are invariant. Define Γ$_{1}$ = { ( y$_{1}$, y$_{2}$ ) | y$_{1}$ = exp(0 . 00025 π ) , 0 ≤ y$_{2}$ ≤ y$_{2}$ ( θ$_{1}$, 0 , (0 , ¯ y$_{2}$ )) } , and Γ$_{2}$ = { ( y$_{1}$, y$_{2}$ ) | y$_{1}$ = 0 , y$_{2}$ ( θ$_{2}$, 0 , − R$_{1}$y$_{2}$ (( θ$_{1}$, 0 , (0 , ¯ y$_{2}$ ))) $^{2}$) ≤ y$_{2}$ ≤ 0 } . The boundary of the curve, Γ = Γ$_{1}$ ∪ Γ$_{2}$ , has of four Figure 1: The region G for system (3.14) is depicted in details. The curves of discontinuity Γ = Γ$_{1}$ ∪ Γ$_{2}$ and ˜ Γ = ˜ Γ$_{1}$ ∪ ˜ Γ$_{2}$ are drawn as vertical lines in red and green, respectively and the grazing orbit in magenta. Z Y Γ ∼ Γ ∼ Γ Γ ∼ ∼ Q Q P P P 2 1 1 2 1 2 2 1 y* 1 y 2 y 2 y 1 2 13