Advances in development of the analytical dynamics of the hereditary discrete systems

Abstract

Research results in area of dynamics of hereditary discrete systems, obtained by authors of this paper, are presented and generalized in the paper, which contains first completed presentation of the analytical dynamics of hereditary discrete systems. Two classes of dynamically defined and undefined hereditary systems are defined and considered by introducing corresponding restrictions. Main results of dynamics of hereditary discrete systems are presented with new applications important to engineering and sciences. Analogy between hereditary interactions and reactive forces in systems of automatic control is identified and a possibility to extend theory of analytical dynamics of hereditary systems to mechanical systems with automatic control is pointed out.