2016/08/31 by Roman Ya. Matsyuk
Mathematics · #math.GM #msc:49N45 #msc:49S05 #msc:53B50 #msc:70E99 #msc:70G65 #msc:70H50 #msc:83A05
published as The Inverse Problem of the Calculus of Variations [Atlantis Studies in Variational Geometry, Vol. 2 (2015)], p.75-102 · Corrected formulae on pp. 10 and 15. arXiv admin note: substantial text overlap with arXiv:1604.08451. Corrected formulae in V2:(3.9); (3.31); first of Proposition 3.6
arxiv created 2017/08/21 · arxiv updated 2017/08/22
Tools of the intrinsic analysis on manifolds, helpful in solving the invariant inverse problem of the calculus of variations are being presented comprising a combined approach which consists in the simultaneous imposition of symmetry principles and the inverse variational problem considerations in terms of vector-valued differential forms. In three-dimensional space-time we obtain a unique (covector) third-order Poincaré-invariant variational equation, which then is identified with the motion of a free relativistic top in flat three-dimensional space-time.