Classical spectrum generating algebra of the Kepler–Coulomb system and action-angle variables

The classical spectrum generating algebra for the one-dimensional Kepler–Coulomb system is computed and a set of two corresponding constants of motion depending explicitly on time is obtained. Such constants supply the solution to the motion in an algebraic way. The connection of the spectrum generating algebra and the action-angle variables of the system is also shown. -- Highlights: ► The spectrum generating algebra for classical (and quantum) 1D Kepler–Coulomb problem is constructed. ► It allows to find constants of motion depending explicitly on time. ► It leads to an algebraic solution of the motion. ► This algebra is related to the action-angle variables of the classical system.