Parabolic coordinates angle

A different set of coordinates for three atoms in 3-dimensional space has been introduced by Shipsey (1969, 1972). This set is intended to treat in an optimum manner reaction paths with small radius of curvature and seems useful for systems with a bent intermediate configuration. Euler angles are introduced to relate space-fixed and body-fixed frames, and parabolic coordinates are defined in this last frame. The coordinates are illustrated for the reaction 1 eO + 14N 1 sO - 1 sO + 14N 160, and it is shown that the orientation coordinate for relative motion becomes the bending normal coordinate of N02 in the interaction region. 

The confinement of a three-dimensional hydrogen atom by a dihedral angle, defined by its meridian half-planes — 0 = 0 and = o in spherical, parabolic and prolate spheroidal coordinates — is the natural extension of the confinement by an angle of the two-dimensional hydrogen atom... 

Fig. 20-2 (a) Coordinates for describing the fields of the beam incident on the endface and (b) the fraction of total power of a Gaussian beam entering the modes of an infinite parabolic-profile fiber as a function of the tilt angle 0.. The orientation of the Gaussian beam is shown for (c) on-axis, (d) tilted and (e) offset illumination. 

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