How to recover a Lagrangian using the homogeneous variational bicomplex
نویسنده
چکیده
We show how the homogeneous variational bicomplex provides a useful formalism for describing a number of properties of single-integral variational problems, and we introduce a subsequence of one of the rows of the bicomplex which is locally exact with respect to the variational derivative. We are therefore able to recover a Lagrangian from a set of equations given as a variationally-closed differential form. As an example, we show how to recover a first-order Lagrangian from a suitable set of second-order equations.
منابع مشابه
Homogeneous variational complexes and bicomplexes
We present a family of complexes playing the same rôle, for homogeneous variational problems, that the horizontal parts of the variational bicomplex play for variational problems on a fibred manifold. We show that, modulo certain pullbacks, each of these complexes (apart from the first one) is globally exact. All the complexes may be embedded in bicomplexes, and we show that, again modulo pullb...
متن کاملBalance Systems and the Variational Bicomplex
In this work we show that the systems of balance equations (balance systems) of continuum thermodynamics occupy a natural place in the variational bicomplex formalism. We apply the vertical homotopy decomposition to get a local splitting (in a convenient domain) of a general balance system as the sum of a Lagrangian part and a complemental “pure non-Lagrangian” balance system. In the case when ...
متن کاملDifferential Geometry
We discuss intrinsic aspects of Krupka's approach to nite{order variational sequences. We recover in an intrinsic way the second{order varia-tional calculus for aane Lagrangians by means of a natural generalisation of rst{ordertheories. Moreover, we nd an intrinsic expressionfor the Helmholtz morphism using a technique introduced by Koll a r that we have adapted to our context. Introduction The...
متن کاملLagrangian Formalism over Graded Algebras
This paper provides a description of an algebraic setting for the Lagrangian formalism over graded algebras and is intended as the necessary first step towards the noncommutative C-spectral sequence (variational bicomplex). A noncommutative version of integration procedure, the notion of adjoint operator, Green’s formula, the relation between integral and differential forms, conservation laws, ...
متن کاملPreprint SISSA 93/94/FM mp arc 94{??? hep-th/9407037 LAGRANGIAN FORMALISM OVER GRADED ALGEBRAS
This paper provides a description of an algebraic setting for the Lagrangian formalism over graded algebras and is intended as the necessary rst step towards the noncommutative C-spectral sequence (variational bicomplex). A noncommutative version of integration procedure, the notion of adjoint operator, Green's formula, the connection between integral and di erential forms, conservation laws, E...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006