Open AccessVariational principle for local fields
Author(s) -
М. Б. Гавриков
Publication year - 2021
Publication title -
preprint/preprinty ipm im. m.v. keldyša
Language(s) - English
Resource type - Journals
eISSN - 2071-2901
pISSN - 2071-2898
DOI - 10.20948/prepr-2021-14
Subject(s) - variational principle , transversality , mathematics , principle of least action , calculus of variations , action (physics) , lagrangian , euler equations , hamilton's principle , luke's variational principle , mathematical analysis , class (philosophy) , elasticity (physics) , classical mechanics , equations of motion , physics , computer science , quantum mechanics , artificial intelligence , thermodynamics
The simplest variational problems (with free, fixed boundaries, the Bolz problem) in Banach spaces are considered. Necessary conditions for a local extremum in these problems are derived. An important class of Lagrangian mechanical systems is considered – local loaded fields, for which the Lagrangian has the form of an integral functional. Necessary conditions for the action functional – the Euler-Ostrogradsky equations and transversality conditions – are obtained. The equations of the theory of elasticity and Maxwell electrodynamics are derived from the variational principle for local fields.