2021/01/02 by Jean de Dieu Maniraguha, Krzysztof Marciniak, Maniraguha, Jean de Dieu +3
Chemistry · Physics and Astronomy · #37J35 (primary) #70H15 (secondary) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics
paper · pdf · doi:10.48550/arxiv.2101.00444
openalex publication_date 2021/01/02 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28
In this paper we discuss two canonical transformations that turn Stäckel separable Hamiltonians of Benenti type into polynomial form: transformation to Viète coordinates and transformation to Newton coordinates. Transformation to Newton coordinates has been applied to these systems only very recently and in this paper we present a new proof that this transformation indeed leads to polynomial form of Stäckel Hamiltonians of Benenti type. Moreover we present all geometric ingredients of these Hamiltonians in both Viète and Newton coordinates.