Open AccessConstruction of the destination set of a dynamic system in $\mathbb{R}^3$
Author(s) -
D. G. Kartashov,
М. С. Таірова
Publication year - 2021
Publication title -
doslìdžennâ v matematicì ì mehanìcì
Language(s) - English
Resource type - Journals
ISSN - 2519-206X
DOI - 10.18524/2519-206x.2020.2(36).233801
Subject(s) - intersection (aeronautics) , convex hull , hyperplane , differential inclusion , set (abstract data type) , function (biology) , point (geometry) , differential (mechanical device) , mathematics , convex set , computer science , dynamical systems theory , mathematical optimization , regular polygon , algorithm , combinatorics , convex optimization , geometry , engineering , physics , quantum mechanics , evolutionary biology , biology , programming language , aerospace engineering
The article proposes two algorithms for the numerical construction of the convex hull of a set in three-dimensional space using its support function. The first uses the hyperplane intersection method to find the pivot points of a set. The second one is based on the deformation function and allows you to find an arbitrary point of the convex hull of a set, which is convenient in many applications. The algorithms are compared, and asymptotic complexities are found. The application of the proposed apparatus to finding the destination set of dynamical systems is shown. The dynamic system will be based on differential inclusion.