The classical dynamics of three particles in hyperspherical coordinates@fa@f)

摘要

Classical dynamics of the three body problem, formulated in hyperspherical coordinates, is investigated. Hamiltonrsquo;s equations of motion are derived and then reduced from 12th order to eighth order. In addition to the general case in which the system moves in threehyphen;dimensional space, the special cases of planar motion, collinear motion, and zero angular momentum motion are studied and related. A brief description of the theory of small amplitude vibrations and normal modes in hyperspherical coordinates is also presented.