Izv. Saratov Univ. Math. Mech. Inform., 2014, Volume 14, Issue 2, Pages 199–209
This article is cited in 1 scientific paper (total in 1 paper)
On a form of the first variation of the action integral over a varied domain
V. A. Kovaleva, Yu. N. Radayevb
a Moscow City Government University of Management, 28, Sretenka str., 107045, Moscow, Russia
b Institute for Problems in Mechanics of RAS, 101-1, Vernadskogo ave., 119526, Moscow, Russia
Field theories of the continuum mechanics and physics based on the least action principle are considered in a unified framework. Variation of the action integral in the least action principle corresponds variations of physical fields while space-time coordinates are not varied. However notion of the action invariance, theory of variational symmetries of action and conservation laws require a wider variation procedure including variations of the space-time coordinates. A similar situation is concerned to variational problems with strong discontinuities of field variables or other a priori unknown free boundaries which variations are not prohibited from the beginning. A form of the first variation of the action integral corresponding variations of space-time coordinates and field variables under one-parametrical transformations groups is obtained. This form is attributed to $4$-dimensional covariant formulations of field theories of the continuum mechanics and physics. The first variation of the action integral over a varied domain is given for problems with constraints. The latter are formulated on unknown free boundaries.
field, action, least action principle, field equations, transformation group, Lie group, infinitesimal generator, variation, varied domain, constraint.
PDF file (243 kB)
V. A. Kovalev, Yu. N. Radayev, “On a form of the first variation of the action integral over a varied domain”, Izv. Saratov Univ. Math. Mech. Inform., 14:2 (2014), 199–209
Citation in format AMSBIB
\by V.~A.~Kovalev, Yu.~N.~Radayev
\paper On a~form of the first variation of the action integral over a~varied domain
\jour Izv. Saratov Univ. Math. Mech. Inform.
Citing articles on Google Scholar:
Related articles on Google Scholar:
This publication is cited in the following articles:
E. V. Murashkin, Yu. N. Radayev, “On a micropolar theory of growing solids”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 24:3 (2020), 424–444
|Number of views:|