2011/07/26 by Mahouton Norbert Hounkonnou, Hounkonnou, Mahouton Norbert, Pascal Dkengne Sielenou +1
Computer Science · Engineering · Mathematics · Physics and Astronomy · #35A15 #35A40 #49-01 #49J10 #49J40 #Applied mathematics #Composite Structure Analysis and Optimization #Conjugate points #Contact Mechanics and Variational Inequalities #Dynamics and Control of Mechanical Systems #FOS: Physical sciences #Lagrangian #Legendre polynomials #Mathematical Physics (math-ph) #Mathematical analysis #Mathematics #Order (exchange) #Variable (mathematics) #Vector-valued function #math-ph #math.MP #msc:35A15 #msc:35A40 #msc:49-01 #msc:49J10 #msc:49J40
paper · pdf · doi:10.48550/arxiv.1107.5344
published in arXiv (Cornell University) (Cornell University)
arxiv created 2011/07/26 · openalex publication_date 2011/07/26 · arxiv updated 2011/07/28 · openalex created_date 2022/08/29 · openalex updated_date 2026/07/28
This paper addresses both necessary and relevant sufficient extremum conditions for a variational problem defined by a smooth Lagrangian, involving higher derivatives of several variable vector valued functions. A general formulation of first order necessary extremum conditions for variational problems with (or without) constraints is given. Global Legendre second order necessary extremum conditions are provided as well as new general explicit formula for second order sufficient extremum condition which does not require the notion of conjugate points as in the Jacobi sufficient condition.