Formalization of dynamic systems investigation problems

Abstract

Calculus and operational calculus. Isaac Newton, the great Renaissance thinker, made the first mathematical model of a dynamic system. In “Mathematical Beginnings of Natural Philosophy” (1687) he described the free motion of celestial objects with the use of differential equations. Practical use of calculus began at that time. Newton shares the founders’ laurels with his great contemporary Leibnitz. But the dynamic system described by Newton was uncontrollable, and its motion could not be modified by man’s will. However, the transition to controlled dynamic systems connected with interposition of the inhomogeneous differential equations, was a quite natural step and was soon carried out.