44 citations · 103 across the 13 of their papers we have counts for
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The Smorodinsky-Winternitz potential revisited
Roman G. Smirnov, Amelia L. Yzaguirre
We employ joint invariants of Killing two-tensors defined in the Euclidean plane to characterize the Smorodinsky-Winternitz potential and explain the geometric meaning of its arbit…
Equivalence problem for the orthogonal webs on the sphere
Caroline Cochran, Raymond G. McLenaghan, Roman G. Smirnov
We solve the equivalence problem for the orthogonally separable webs on the three-sphere under the action of the isometry group. This continues a classical project initiated by Ole…
Hamilton-Jacobi Theory and Moving Frames
Joshua D. MacArthur, Raymond G. McLenaghan, Roman G. Smirnov
The interplay between the Hamilton-Jacobi theory of orthogonal separation of variables and the theory of group actions is investigated based on concrete examples.
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.
Covariants,joint invariants and the problem of equivalence in the invariant theory of Killing tensors defined in pseudo-Riemannian spaces of constant curvature
Roman G. Smirnov, Jin Yue
The invariant theory of Killing tensors (ITKT) is extended by introducing the new concepts of covariants and joint invariants of (product) vector spaces of Killing tensors defined…