Elastic collision dynamics trajectories

The dynamics of the two-particle problem can be separated into center-of-mass motion and relative motion with the reduced mass /i = morn s/(rnp + me), of the two particles. The kinetic energy of the relative motion is a conserved quantity. The outcome of the elastic collision is described by the deflection angle of the trajectory, and this is the main quantity to be determined in the following. The deflection angle, X, gives the deviation from the incident straight line trajectory due to attractive and repulsive forces. Thus, x is the angle between the final and initial directions of the relative velocity vector for the two particles. 

Two of the most common classes of particle-dynamic simulations are termed hard-particle and soft-particle methods. Hard-particle methods calculate particle trajectories in response to instantaneous, binary collisions between particles, and allow particles to follow ballistic trajectories between collisions. This class of simulation permits only instantaneous contacts and is consequently often used in rapid flow situations such as are found in chutes, fluidized beds, and energetically agitated systems. Soft-particle methods, on the other hand, allow each particle to deform elastoplastically and compute responses using standard models from elasticity and tribology theory. This approach permits enduring particle contacts and is therefore the method of choice for mmbler apphcations. The simulations described in this chapter use soft-particle methods and have been validated and found to agree in detail with experiments. 

Before we turn to discussion of intermolecular potentials that depend also on the orientation of the colliding molecules and their internal deformations, we need to examine the dynamics of the collision of structureless particles. For this simple case the only outcome of the collision is tiiat the particles deflect one another from their original trajectories. The colhsion is said to be elastic. 

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