| Majid Abbasov, Anna Belenok, Anna Gorbunova Obtaining a parametric equation for the road trajectory which is optimal in terms of construction costs |
|---|
| Abstract. There are different approaches to define trajectory that is optimal from the point of view of construction costs. We study the problem of obtaining a parametric equation of the cost-optimal trajectory for the road connecting two points on an initially given terrain. By means of mathematical modelling approach we construct the integral cost functional, which arguments are parametric functions describing the trajectory. Therefore, we get the problem of the calculus of variations, the solution of which defines the most cost-effective way. We derive the optimality condition which has a form of a system of integro-differential equations. We solve the equations from the resulting system using the Galerkin method. The optimal solution is presented as linear combination of the first n functions of a system of twice continuously differentiable compactly supported functions on a given interval. The paper also presents the results of numerical experiments for various surfaces on which the road is laid. |
| Keywords: Calculus of variations, Mathematical modelling, Integro-differential equation, Shooting method, Linearization, Optimal trajectory |
 Download PDF |
| DOI: https://doi.org/10.54381/itta2024.01 |