Classical scattering of structureless particles

Dynamics means the description of the motion under the action of forces. For our problem of two particles, this means solving Newton s equation of motion for the relative motion 

Our first task is to examine the time evolution of the vector R. This will uncover a conservation condition that was already used by Newton to explain Kepler s 

By the definition of a vector product, L is a vector perpendicular to the plane defined by the position and momentum vectors. 

For a colhsion of structnreless particles, the acceleration is in the direction of the relative position vector R, cf Eq. (4.1). The chain rnle then shows that the vector L is not changing with time  

Both terms in Eq. (4.3) vanish, since, in either term, the two vectors that are vector multiplied are parallel to one another. 

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