Orbital evolutions of the semi-major axis, resonant angles, and eccentricity as functions of time. At the top of the first plot, we indicate the corresponding particle. The results in the first column are for a particle with initial conditions a = 3.8398 AU and e = 0.00070. The second column is for a particle with initial conditions a = 10.0980 AU and e = 0.00049. Note that the evolution of φ (second plot) shows that the P1 and P2 particles cross the two-body mean motion resonance and that the libration of the φ angle is evidence of an association between the orbits and the resonances.