Thereareabout500booksonvariationalprinciples. Theyareconcernedmostlywith
the mathematical aspects of the topic. The major goal of this book is to
discuss the physical origin of the variational principles and the
intrinsic interrelations between them. For example, the Gibbs principles
appear not as the rst principles of the theory of thermodynamic
equilibrium but as a consequence of the Einstein formula for
thermodynamic uctuations. The mathematical issues are considered as long
as they shed light on the physical outcomes and/or provide a useful
technique for direct study of variational problems.
Thebookisacompletelyrewrittenversionoftheauthor'smonographVariational
Principles of Continuum Mechanics which appeared in Russian in 1983. I
have been postponing the English translation because I wished to include
the variational pr- ciples of irreversible processes in the new edition.
Reaching an understanding of this subject took longer than I expected.
In its nal form, this book covers all aspects of the story. The part
concerned with irreversible processes is tiny, but it determines the
accents put on all the results presented. The other new issues included
in the book are: entropy of microstructure, variational principles of
vortex line dynamics, va- ational principles and integration in
functional spaces, some stochastic variational problems, variational
principle for probability densities of local elds in composites with
random structure, variational theory of turbulence; these topics have
not been covered previously in monographic literature.
