Lepagean 2-forms in higher order Hamiltonian mechanics. I: Regularity. (English) Zbl 0637.58002

Krupková, Olga

Arch. Math., Brno 22, 97-120 (1986).

From the author’s summary: “The notion of the Lepagean equivalent of an Euler-Lagrange form is introduced. Applied to the higher order Hamiltonian mechanics, it enables one to reformulate the Hamilton theory for the whole set of equivalent Lagrangians. A generalization of the standard regularity condition is obtained and a general Legendre transformation is proposed and investigated.”

Reviewer: Yu.E.Gliklikh

MSC:

37J99	Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
70H05	Hamilton’s equations
58E30	Variational principles in infinite-dimensional spaces

Keywords:

Lepagean form; locally variational form; Euler-Lagrange form; Hamiltonian mechanics; Legendre transformation