Principal-axis Hyperspherical Description of N-particle Systems - Classical Treatment
(1991) Physical review. A, Atomic, molecular, and optical physics — Vol. 44, n° 2, p. 1328-1351 (1991)
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- Principal-axis hyperspherical coordinates (made up of one hyperradius and 3N - 7 angles as internal coordinates) and three Eulerian angles as external (rotational) coordinates are defined from the Eckart coordinate system [Phys. Rev. 46, 383 (1934)]. They can describe any N-particle system. The exact classical Hamiltonian of the system in terms of these coordinates is derived, and it is remarkably simple. The quantization of this Hamiltonian is deferred for future study.
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Chapuisat, X., & Nauts, A. (1991). Principal-axis Hyperspherical Description of N-particle Systems - Classical Treatment. Physical review. A, Atomic, molecular, and optical physics, 44(2), 1328-1351. https://doi.org/10.1103/PhysRevA.44.1328 (Original work published 1991)