GROUP-THEORETIC METHODS IN MECHANICS AND APPLIED MATHEMATICS

This book contains the basics of group analysis of differential equations and its applications to various problems on nonlinear mechanics and physics. The consistent presentation of Lie group theory is illustrated by plentiful examples. For the first time the systematic group analysis of main postulates of classical and relativistic mechanics is given. Symmetries and conservation laws of differential equations are studied. Specific equations and problems of mechanics and physics are considered and exact solutions are given for equations of dynamics of ridgid body, heat transfer equations, wave equations, equations of hydrodynamics, the Thomas-Fermi equations, etc.
Special attention is paid to the application of group analysis to developing asymptotic methods of applied mathematics in problems with small parameter. The methods developed are used to solve basic equations (Van Der Pol's equation, Duffing equation, etc) encountered in the theory of nonlinear oscillations. This book will be valuable source for a wide range of scientists, engineers and students in the fields of applied mathematics, mechanics and physics.