Replace the right hand sides of [math]x_1\left(t\right)[/math], [math]y_1\left(t\right)[/math], [math]x_2\left(t\right)[/math], and [math]y_2\left(t\right)[/math]so that [math]P_1[/math] starts at A, goes to B along the parabola, then back to C, and then goes to D, while [math]P_2[/math] travels the same way, but changing directions more suddenly.