Variational principle for local fields | Zendy

Михаил Борисович Гавриков | Zendy

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Variational principle for local fields

Author(s) -

Михаил Борисович Гавриков

Publication year - 2021

Publication title -

keldysh institute preprints

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.

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