2013/03/07 by Yuri L. Sachkov, Yuri Sachkov, Sachkov, Yuri +3
Engineering · Mathematics · #49J15 #65D07 #74B20 #74K10 #93B29 #93C10 #Advanced Numerical Analysis Techniques #FOS: Mathematics #History and Theory of Mathematics #Mathematical and Computational Methods #Optimization and Control (math.OC) #math.OC #msc:49J15 #msc:65D07 #msc:74B20 #msc:74K10 #msc:93B29 #msc:93C10
paper · pdf · doi:10.48550/arxiv.1303.1746
arxiv created 2013/03/07 · openalex publication_date 2013/03/07 · arxiv updated 2013/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The classical Euler's problem on optimal configurations of elastic rod in the plane with fixed endpoints and tangents at the endpoints is considered. The global structure of the exponential mapping that parameterises extremal trajectories is described. It is proved that open domains cut out by Maxwell strata in the preimage and image of the exponential mapping are mapped diffeomorphically. As a consequence, computation of globally optimal elasticae with given boundary conditions is reduced to solving systems of algebraic equations having unique solutions in the open domains. For certain special boundary conditions, optimal elasticae are presented.