On hyperspherical coordinates and mapping the internal configurations of a three body system

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Abstract
A procedure for mapping the internal configurations of a three body system to points in a three dimensional ’’configuration space’’ is presented. The mapping is based on a modified version of the Smith–Whitten symmetric hyperspherical coordinate system. Several years ago, Kuppermann developed a mapping procedure based on a different hyperspherical coordinate system. Transformation equations relating these two mappings are derived. A comparison shows that the present method produces maps identical to Kuppermann’s method. The coordinate axes in configuration space, however, are rotated by 90 degrees so that the z axis is coincident with the axis of kinematic rotation.