Izvestiya of Saratov University.
ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

Lie group

On a form of the first variation of the action integral over a varied domain

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.