Method for finding the cost-optimal road trajectory on the surface of the terrain

The paper studies a method for finding the cost-optimal trajectory of a road connecting two points on a given terrain. Situations are considered when the cost of delivery of materials is a constant value, as well as a more general formulation of the problem, in which the cost of delivery depends on the coordinate of a point. In each case, an integral functional is constructed cost, the argument in which is a function that describes the trajectory of the path. The Ritz method is used to find an approximate solution. It is set analytically, in the form of a trigonometric polynomial, which increases the convenience of processing and further research of the results obtained in comparison with the numerical solution of the necessary conditions for the extremum of the investigated functional. The paper also discusses the problem of convergence. Illustrative examples are given.