The role of variational principles of mechanics in the study of the evolution of non-conservative dynamical systems

The article covers the basics of variational principles of mechanics applied to a material point is a brief historical background of variational methods mechanics, considered classical variational problem with fixed ends, shows the relationship of the law of conservation of energy to the principle of stationary action, as well as obtaining the characteristic function of a non-conservative system as an example of a mechanical system Linear friction. On the basis of Noether’s theorem, shows the relationship of the first integral of the mechanical system, with its characteristic function, and interpretation made the first integral non-conservative mechanical system with linear friction.