Computer Modeling of Discrete Systems in the Case of Linear and non‐Linear Restrictions on the Optimal Speed of the Aircraft Based on the Lagrange Method

The paper of the report represents the study dedicated to the main link of the aircraft flight speed to the minimal time of the air transportation process. The simplest problem of the aviation transportation technologies fundamental factors optimization models the considered process of the delivery and it makes an attempt to the process theoretical description. Two segment air traffic elementary chain of supply is implied at the presented research. The algorithm, which is used for calculating the objective parameters of the aircraft motion, is developed. Approaches to aircraft speed optimization are used. The speed of the delivery by the aircraft at each of the segments have been conditionally optimized. The objective value is the time of delivery. The aircraft speeds are subject to both linear and nonlinear constraints. The influence of the speeds' variations upon the conditionally minimal objective delivery time values are studied. Theoretical contemplations are conducted in the framework of the Lagrange uncertainty multipliers implementation. The hypothetical provisions of the derived mathematical models are illustrated with the help numerical simulation. The part of the computer modeling is conducted on the Mathcad platform at the educational and scientific laboratory "Modeling of transport systems and processes" of National Aviation University. The necessary diagrams are plotted. The obtained results of both theoretical study and computer simulation allows construction of optimal delivery chains with a better determination of the exchange point location.