一次元弾性衝突の計算機シミュレーション

概要

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Consider N material particles constrained to remain on the x-axis and connected with each other by (N-l) elastic springs. If this system travels with a given velocity in one direction and collides with an elastic wall located on some definite point, it will be reflected in the opposite direction. The equations of motion can be numerically integrated by the Runge-Kutta Method and the positions and velocities at any moment of all the particles can be obtained. The durations of the collision processes thus calculated turn out to be about 1.5 to 2.1 times as long as the times predicted from one round-trip of the stress waves over the length of the particle system. A system of N particles has N degrees of freedom, and has N normal modes, each being characterized with eigen-vector and eigen-frequency. During the collision process, transference of mechanical energy among different nomal modes takes place, and the coefficient of restitution is usually expected to be less than one. If we reverse the velocities of all the particles at some arbitrary instant after one collision, then we find that the coefficient of restitution observed in the second collision is just the inverse of the coefficient observed in the first collision. The conservation of mechanical energy is thus proved bv these time-reversal experiment.
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