Hamilton formalism and variational principle construction

P. Ván, B. Nyíri

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

It is widely accepted that a variational principle cannot be constructed for an arbitrary differential equation; a rigorous mathematical condition shows which equations can have a variational formulation. On the other hand, the importance for variational principles in various fields of physics resulted in several methods to circumvent this condition and to construct another type of variational principles for any differential equation. In this paper the common origin of the considered methods is investigated, and a generalized Hamiltonian formalism is formulated. Additionally, constructive algorithms are given by different methods to construct variational principles. Simple examples are presented to make construction methods more transparent: several Lagrangians are constructed for the different forms of the Maxwell equations and for the extended heat conduction equation.

Original languageEnglish
Pages (from-to)331-354
Number of pages24
JournalAnnalen der Physik (Leipzig)
Volume8
Issue number4
DOIs
Publication statusPublished - Jan 1 1999

Keywords

  • Hamilton formalism
  • Maxwell equations
  • Variational principles

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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