2012/12/31 by Paul Popescu · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Cotangent bundle #Equivalence (formal languages) #Geometry #Hamiltonian (control theory) #Lagrangian #Mathematical analysis #Mathematics #Normal bundle #Pure mathematics #Tangent #Tangent bundle #Tangent cone #Tangent space #Tangent vector #Trigonometric functions #Unit tangent bundle #Vector bundle #math-ph #math.MP #msc:53C80 #msc:53D35 #msc:70G45 #msc:70H03 #msc:70H06 #msc:70H07 #msc:70H30 #msc:70H50
paper · pdf · doi:10.1016/j.geomphys.2013.12.008
published in Journal of Geometry and Physics 77, 113-130 (Elsevier BV) · 30 pages, Accepted for publication in Journal of Geometry and Physics
arxiv created 2013/12/17 · openalex publication_date 2014/01/03 · arxiv updated 2014/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The aim of the paper is to study some dynamic aspects coming from a tangent form, i.e. a time dependent differential form on a tangent bundle. The action on curves of a tangent form is natural associated with that of a second order Lagrangian linear in accelerations, while the converse association is not unique. An equivalence relation of tangent form, compatible with gauge equivalent Lagrangians, is considered. We express the Euler-Lagrange equation of the Lagrangian as a second order Lagrange derivative of a tangent form, considering controlled and higher order tangent forms. Hamiltonian forms of the dynamics generated are given, extending some quantization formulas given by Lukierski, Stichel and Zakrzewski. Using semi-sprays, local solutions of the E-L equations are given in some special particular cases.