Helmholtz's inverse problem of the discrete calculus of variations

Loïc Bourdin (1) , Jacky Cresson (2, 1)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 IMCCE - Institut de Mécanique Céleste et de Calcul des Ephémérides

We derive the discrete version of the classical Helmholtz's condition. Precisely, we state a theorem characterizing second order finite differences equations admitting a Lagrangian formulation. Moreover, in the affirmative case, we provide the class of all possible Lagrangian formulations.

Domaines: Systèmes dynamiques [math.DS]; Optimisation et contrôle [math.OC]

Loïc Bourdin, Jacky Cresson. Helmholtz's inverse problem of the discrete calculus of variations. Journal of Difference Equations and Applications, 2013, 19 (9), pp.1417-1436. ⟨10.1080/10236198.2012.754435⟩. ⟨hal-00866945⟩