Abstract
Group analysis of differential equations uses the Lie theory of correspondence between continuous transformation groups and Lie algebras of first-order differentiation operators. Differential equations of mechanics necessarily admit an extensive group of transformations. Lie theory studies the structure of the algebra of this group. The group analysis of the equations of mechanics uses the structure of the admissible algebra to produce submodels and exact solutions, to study the boundary value problems of submodels and the behavior of the mechanical medium for exact solutions. The main tasks of group analysis are formulated and simple examples of their solutions are given.
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