Homogeneous Stäckel-type systems
Completely integrable systems of Stäckel type are holonomic systems in the phase space \(\mathbb{R}^{2n}\) with Hamiltonian \[ H= \sum_{j=1}^n g_j (q_1,\dots, q_n) (p_j^2+ V_j(q_j)), \] where \(\{p_j, q_j\}\) are canonical variables in \(\mathbb{R}^{2n}\). The author proves that the Stäckel matrix is the derivative of the Abel mapping. The author constructs the Lax representation and studies its properties. Using the representation he constructs curvilinear orthogonal coordinate systems in a flat space and two classes of canonical coordinate transformations related to these systems.
scientific article; zbMATH DE number 1466068
scientific article