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Hamilton formalism and variational principle construction
Author(s) -
Ván P.,
Nyíri B.
Publication year - 1999
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/(sici)1521-3889(199904)8:4<331::aid-andp331>3.0.co;2-r
Subject(s) - variational principle , variational integrator , constructive , formalism (music) , hamiltonian (control theory) , variational analysis , differential equation , luke's variational principle , mathematics , hamilton's principle , variational method , calculus of variations , physics , classical mechanics , mathematical analysis , computer science , mathematical optimization , equations of motion , quantum mechanics , art , musical , voltage , integrator , visual arts , process (computing) , operating system
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.