On the gauge structure of classical mechanics

DOI10.1080/00411450008205861zbMath0968.70014OpenAlexW2011776252WikidataQ126240901 ScholiaQ126240901MaRDI QIDQ4488723

Enrico Massa, Paolo Lorenzoni, Enrico M. Pagani

Publication date: 5 September 2001

Published in: Transport Theory and Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00411450008205861

zbMATH Keywords

configuration spacegauge transformationsphase spaceconnectionLagrangian mechanicsvelocity spaceLagrangian bundlecurvature 2-formCartan 2-formbundle of affine scalarsco-Hamiltonian bundleco-Lagrangian bundleHamiltonian bundleinvariance of Euler-Lagrange equation

Mathematics Subject Classification ID

Hamilton's equations (70H05) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems (70S05) Lagrange's equations (70H03)

Related Items

ON THE GAUGE STRUCTURE OF THE CALCULUS OF VARIATIONS WITH CONSTRAINTS ⋮ Jacobi structures on affine bundles ⋮ Legendre transformation and analytical mechanics: A geometric approach ⋮ On the Herglotz variational problem ⋮ The non-holonomic Herglotz variational problem ⋮ Homogeneous variational problems and Lagrangian sections ⋮ AV-differential geometry: Euler-Lagrange equations ⋮ AV-differential geometry: Poisson and Jacobi structures

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Reduction of degenerate Lagrangian systems
• Equations of motion, commutation relations and ambiguities in the Lagrangian formalism
• A new look at second-order equations and Lagrangian mechanics
• A geometrical version of the Helmholtz conditions in time-dependent Lagrangian dynamics
• Lagrangians for spherically symmetric potentials