Lagrangian Operators with Higher Derivatives
F. Talamucci *
DIMAI Dept. of Mathematics and Informatics, University of Florence, Viale G. B. Morgagni 67/a 50134, Italy.
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: Lagrange's equations, higher order theories, lagrangian formalism for holonomic systems