Models and Methods for Three External Ballistics Inverse Problems

TL;DR

This paper introduces models and a unified numerical method for solving three inverse problems in external ballistics involving optimal gun barrel orientation within visibility constraints, with applications demonstrated through numerical experiments.

Contribution

It presents a novel unified numerical approach for three external ballistics inverse problems with non-smooth objective functions and visibility constraints.

Findings

Effective numerical method developed for the problems.

Successful numerical experiments demonstrate applicability.

Models accommodate non-smooth, non-convex constraints.

Abstract

We consider three problems of selecting optimal gun barrel direction (or those of selecting optimal semiaxis position) when firing an unguided artillery projectile on the assumption that the gun barrel semiaxis can move in a connected nonconvex cone having a non-smooth lateral surface and modelling visibility zone restrictions. In the first problem, the target is in the true horizon plane of the gun, the second and the third problems deal with some region of 3D space. A distinctive feature of the models is that the objective functions are $\varepsilon$-Lipschitz ones. We have constructed a unified numerical method to solve these problems based on an algorithm of projecting a point onto $\varepsilon$-Lipschitz level function set. A computer program has been based on it. A series of numerical experiments on each problem has been carried out. App. 1.