Analytical Dynamics

Abstract

The aim of the present and the following chapters is to set forth the results of investigation on the connection and analogies between the classical analytical dynamics and the theory of optimal control. The theory of optimal control or, more precisely, the theory of control of processes which take place in course of a given period of time, and are described by differential equations, developed as a part of science in the middle of the twentieth century. Its development was associated with a large number of practical problems that arose in diverse spheres of the human activity. This resulted in new problems in the calculus of variations. And solution of these problems stimulated a further growth of this section of mathematical anlaysis. The laying of the initial foundation of the calculus of variations is directly related to the Lagrange-Hamilton integral extremal principles of analytical dynamics, and this connection in the course of development grew weaker and weaker. This is possibly due to the discovery of the fact that the theory of optimal control can be applied to objects other than mechanical systems, and the latter started to be treated simply as a region for application of the new theory.