This article is cited in 7 papers

Applied mathematics

Searching for the cost-optimal road trajectory on the relief of the terrain

M. E. Abbasov^ab, A. S. Sharlay<sup>c

a</sup> St. Petersburg State University, 7–9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
^b Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences, 61, Bolshoy pr. V. O., St. Petersburg, 199178, Russian Federation
^c Military Educational Institute of Logistics named after General of the Army A. V. Khruleov, 1, Suvorovskaya ul., St. Petersburg, 198504, Russian Federation

Abstract: The article analyzes the problem of obtaining the cost-optimal trajectory for building a road. Using the apparatus of mathematical modelling, the authors derive the cost functional, the argument of which is the function that describes the path trajectory. The resulting functional after some additional transformations is written in a simpler form. For the problem of the calculus of variations obtained in this manner, an optimality condition is derived. This condition takes into account the specifics of the constructed functional. Unlike the classical Euler—Lagrange condition, it leads not to a differential, but to an integro-differential equation. An illustrative example of the numerical solution of the obtained equation using the methods of computational mathematics is provided.

Keywords: calculus of variations, optimization, integro-differential equations.

UDC: 517.972.2

MSC: 49K21

Received: December 2, 2020
Accepted: January 15, 2021

DOI: 10.21638/11701/spbu10.2021.101