ABSTRACT
The concept of a conservation law for a differential equation is motivated by the conservation of such quantities as energy, linear and angular momentum, etc. for equations that arise in classical particle mechanics. It has been known for a long time that the conservation laws of classical mechanics are connected with symmetry properties of the physical system. This connection was clearly described in the course of mechanics by C. Jacoby. Noether was the first to combine the methods of the variational calculus with the theory of Lie groups and to formulate a general approach for constructing conservation laws for Euler–Lagrange equations when their symmetries are known. It is this connection that is exhibited by the Noether theorem.
