Lagrangian Operators with Higher Derivatives

A simple formal procedure makes the main properties of the ordinary lagrangian operator extendable to some higher order di erential operators de ned for functions depending on the lagrangian coordinates q and on their derivatives of any order with respect to time. The higher order calculated expressions can provide the lagrangian components, in the classical sense of the Newton's law, for a quite general class of forces. At the same time, the generalized equations of motions recover some of the classical alternative formulations of the Lagrangian equations.