Noether’s Approach to Dynamic Systems

The first Chapter serves as the short introduction in the subject symmetries and variations. The techniques for establishing of conservation laws from the symmetries of the simplest variational functionals are briefly deliberated. A theorem formulated by Emmy Noether’s in 1918 can be summarized in a few words: “To every continuous symmetry of a physical system belongs a conservation law”. Noether’s theorem provides a powerful method for the establishing of the conservation laws form the corresponding symmetries. The actual Chapter summarize the principal applications of Noether’s procedures to the mechanics of systems with the finite and infinite number of degrees of freedom.