44 citations · 49 across the 7 of their papers we have counts for
4 papers · 1 filter
On geometric properties of joint invariants of Killing tensors
Caroline M. Adlam, Raymond G. McLenaghan, Roman G. Smirnov
We employ the language of Cartan's geometry to present a model for studying vector spaces of Killing two-tensors defined in pseudo-Riemannian spaces of constant curvature under the…
A class of superintegrable systems of Calogero type
Roman G. Smirnov, Pavel Winternitz
We show that the three body Calogero model with inverse square potentials can be interpreted as a maximally superintegrable and multiseparable system in Euclidean three-space. As s…
Invariant classification of orthogonally separable Hamiltonian systems in Euclidean space
Joshua T. Horwood, Raymond G. McLenaghan, Roman G. Smirnov
The problem of the invariant classification of the orthogonal coordinate webs defined in Euclidean space is solved within the framework of Felix Klein's Erlangen Program. The resul…
The classical Bertrand-Darboux problem
Roman G. Smirnov
The well-known problem of classical mechanics considered by Bertrand (1857) and Darboux (1901) is reviewed in the context of Cartan's geometry.