<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The formal models of physical systems are typically written in terms of differential equations. A transformation of the variables in a differential equation forms a symmetry group if it leaves the differential equation invariant. Symmetries of differential equations are very important for understanding of their properties. It can be said that the theory of Lie group symmetries of differential equations is general systematic method for finding solutions of differential equations. Despite of this fact, the Lie group theory is relatively unknown in engineering community. The paper is devoted to some important questions concerning this theory and for several equations resulting from the theory of elasticity their Lie group infinitesimal generators are given.</p></abstract>

The formal models of physical systems are typically written in terms of differential equations. A transformation of the variables in a differential equation forms a symmetry group if it leaves the differential equation invariant. Symmetries of differential equations are very important for understanding of their properties. It can be said that the theory of Lie group symmetries of differential equations is general systematic method for finding solutions of differential equations. Despite of this fact, the Lie group theory is relatively unknown in engineering community. The paper is devoted to some important questions concerning this theory and for several equations resulting from the theory of elasticity their Lie group infinitesimal generators are given.

Some Differential Equations of Elasticity and their Lie Point Symmetry Generators

Faculty of Mechanical Engineering, Department of Applied Mechanics and Mechatronics, Technical University of Kosice, Letna 9, 042 00 Kosice, Slovakia

Acta Mechanica et Automatica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

The formal models of physical systems are typically written in terms of differential equations. A transformation of the variables in a differential equation...

Some Differential Equations of Elasticity and their Lie Point Symmetry Generators

Article Category: research article

Published Online: Aug 10, 2014

Page range: 99 - 102

DOI: https://doi.org/10.2478/ama-2014-0018

© 2014 Jozef Bocko et. al.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.