Group analysis of differential equations has applications to various problems in nonlinear mechanics and physics. For the first time, this book gives the systematic group analysis of main postulates of classical and relativistic mechanics. The consistent presentation of Lie group theory is illustrated by plentiful examples. 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 the following equations: dynamics of rigid body, heat transfer, wave, hydrodynamics, Thomas-Fermi and more. The author pays particular attention to the application of group analysis to developing asymptotic methods of applied mathematics in problems with small parameter. The methods are used to solve basic equations (Van Der Pol's equation, Duffing equation, etc.) encountered in the theory of nonlinear oscillations. This book is intended for a wide range of scientists, engineers and students in the fields of applied mathematics, mechanics and physics.

Group analysis of differential equations has applications to various problems in nonlinear mechanics and physics. For the first time, this book gives the systematic group analysis of main postulates of classical and relativistic mechanics. The consistent presentation of Lie group theory is illustrated by plentiful examples. 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 the following equations: dynamics of rigid body, heat transfer, wave, hydrodynamics, Thomas-Fermi and more. The author pays particular attention to the application of group analysis to developing asymptotic methods of applied mathematics in problems with small parameter. The methods are used to solve basic equations (Van Der Pol's equation, Duffing equation, etc.) encountered in the theory of nonlinear oscillations. This book is intended for a wide range of scientists, engineers and students in the fields of applied mathematics, mechanics and physics.

The International Union of Theoretical and Applied Mechanics (IUTAM) initiated and supported an International Symposium on Dynamical Problems for Rigid-elastic Systems and Structures held in 1990 in Moscow, USSR. The Symposium was intended to bring together scientists working in the fields of multibody system dynamics and finite element systems with special emphasis to modeling, simulation, optimization and control. A Scientific Committee was appointed by the Bureau of IUTAM with following members: N.V. Banichuk (USSR). E.J. Haug (USA). Y. Hori (Japan). S. Kaliszky (Hungary), D.M. Klimov (USSR). Chairman, L. Lilov (Bulgaria), F. Niordson (Denmark), B. Roth (USA), W. Schiehlen (Germany), G. Schmidt (Germany), J. Wittenburg (Germany). The chairman invited the participants on recommendation by the Scientific Committee. As a result 48 active scientific participants from 11 countries followed the invitation, and 32 papers were presented in lecture sessions. The available manuscripts were reviewed by the Scientific Committee after the Symposium, and 24 of them are collected in this volume. At the Symposium a tour to the Institute for Problems of Mechanics, USSR Academy of Sciences, was arranged. The scientific lectures were devoted to the following topics: o Modeling and Optimization, o Dynamics of Systems with Elastic Constraints, o Vibrations, o Multibody Systems.