2002/12/31 by Arturo Echeverria-Enrı́quez, A. Echeverría-Enríquez, C. López +7 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Applied mathematics #Classical mechanics #Control and Stability of Dynamical Systems #Covariant Hamiltonian field theory #Covariant transformation #Formalism (music) #Geometry #Hamiltonian (control theory) #Hamiltonian formalism #Hamiltonian mechanics #Hamiltonian system #Lagrangian #Legendre polynomials #Legendre transformation #Mathematical analysis #Mathematical optimization #Mathematical physics #Mathematics #Numerical methods for differential equations #Physics #Quantum mechanics #Rotation formalisms in three dimensions #math-ph #math.DG #math.MP #msc:51P05 #msc:53C05 #msc:53C80 #msc:55R10 #msc:58A20 #msc:58A30 #msc:70S05
paper · pdf · doi:10.1063/1.1628384
published as J.Math.Phys. 45 (2004) 360-380 · LaTeX file, 23 pages. Minor changes have been made. References are updated
openalex publication_date 2003/12/19 · arxiv created 2004/02/13 · openalex created_date 2016/06/24 · arxiv updated 2016/08/16 · openalex updated_date 2026/08/05
The Rusk–Skinner formalism was developed in order to give a geometrical unified formalism for describing mechanical systems. It incorporates all the characteristics of Lagrangian and Hamiltonian descriptions of these systems (including dynamical equations and solutions, constraints, Legendre map, evolution operators, equivalence, etc.). In this work we extend this unified framework to first-order classical field theories, and show how this description comprises the main features of the Lagrangian and Hamiltonian formalisms, both for the regular and singular cases. This formulation is a first step toward further applications in optimal control theory for partial differential equations.