Advances in Theoretical and Mathematical Physics

Volume 26 (2022)

Number 3

Transforming Stäckel Hamiltonians of Benenti type to polynomial form

Pages: 711 – 734



Jean de Dieu Maniraguha (College of Science and Technology, University of Rwanda, Kigali, Rwanda)

Krzysztof Marciniak (Department of Science and Technology, Linköping University, Norrköping, Sweden)

Célestin Kurujyibwami (College of Science and Technology, University of Rwanda, Kigali, Rwanda)


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.

The research of J.D. Maniraguha and C. Kurujyibwami was supported by International Science Programme (ISP, Uppsala University) in collaboration with Eastern Africa Universities Mathematics Programme (EAUMP). The research of K. Marciniak was partially supported by the Swedish International Development Cooperation Agency (Sida) through the Rwanda- Sweden bilateral research cooperation.

Published 22 February 2023