{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:43:22Z","timestamp":1760240602313,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2019,7,26]],"date-time":"2019-07-26T00:00:00Z","timestamp":1564099200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Poznan University of Technology, Faculty of Electrical Engineering","award":["DNPB 04\/45\/SBAD\/0210"],"award-info":[{"award-number":["DNPB 04\/45\/SBAD\/0210"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>The paper presents the application of variational calculus to achieve the optimal design of the open-loop control law in the process of anti-ballistic missile interception task. It presents the analytical results in the form of appropriate Euler\u2013Lagrange equations for three different performance indices, with a simple model of the rocket and the missile, based on the conservation of momentum principle. It also presents the software program enabling rapid simulation of the interception process with selected parameters, parametric analysis, as well as easy potential modification by other researchers, as it is written in open code as m-function of Matlab.<\/jats:p>","DOI":"10.3390\/a12080148","type":"journal-article","created":{"date-parts":[[2019,7,26]],"date-time":"2019-07-26T08:45:39Z","timestamp":1564130739000},"page":"148","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Variational Calculus Approach to Optimal Interception Task of a Ballistic Missile in 1D and 2D Cases"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9456-6704","authenticated-orcid":false,"given":"Dariusz","family":"Horla","sequence":"first","affiliation":[{"name":"Poznan University of Technology, Faculty of Electrical Engineering, Institute of Control, Robotics and Computer Science, 60-965 Poznan, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,7,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1524","DOI":"10.2514\/1.32262","article-title":"Trajectory-Shaping Guidance for Interception of Ballistic Missiles during the Boost Phase","volume":"31","author":"Yakimenko","year":"2008","journal-title":"J. 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