2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58021It is shown that there exists a commuting diagram of mappings between dynamics of classical systems on one side and variational principles for geodesic lines in stationary spacetimes of general relativity on the other. The construction of the mappings is based on classical Routh's and Jacobi's procedures and on corresponding inverse procedures which are reviewed in the paper.Submitted to a prepared volume in celebration of 75-th birthday of Jerzy PlebanskiMathematical PhysicsGeneral Relativity and Quantum CosmologyPrimary: 70H30, 53B30. Secondary: 83C20, 53B50, 83-02text