The classical dynamics of three particles in hyperspherical coordinates

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Abstract
Classical dynamics of the three body problem, formulated in hyperspherical coordinates, is investigated. Hamilton’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 three-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.