Lie algebroid structures and Lagrangian systems on affine bundles

Abstract

As a continuation of previous papers, we study the concept of a Lie algebroid structure on an affine bundle by means of the canonical immersion of the affine bundle into its bidual. We pay particular attention to the prolongation and various lifting procedures, and to the geometrical construction of Lagrangian-type dynamics on an affine Lie algebroid.

28 pages, Latex

References in corpus (3)

• Generalized Lie bialgebroids and Jacobi structures
• Lie algebroid structures on a class of affine bundles
• Some linear Jacobi structures on vector bundles

Cited by in corpus (19)

• Lagrangian submanifolds and dynamics on Lie algebroids
• Dirac Algebroids in Lagrangian and Hamiltonian Mechanics
• Classical field theory on Lie algebroids: Variational aspects
• A unified framework for mechanics. Hamilton-Jacobi equation and applications
• Variational calculus with constraints on general algebroids
• AV-differential geometry: Poisson and Jacobi structures
• A Lie algebroid framework for non-holonomic systems
• Almost Kaehler Ricci Flows and Einstein and Lagrange-Finsler Structures on Lie Algebroids
• AV-differential geometry: Euler-Lagrange equations
• Lagrangian submanifolds and dynamics on Lie affgebroids
• Symmetries of second order differential equations on Lie algebroids
• On the Geometry of the Hamilton-Jacobi Equation and Generating Functions
• AV-differential geometry and Newtonian mechanics
• The Berwald-type linearisation of generalised connections
• Gauge equivalence and conserved quantities for Lagrangian systems on Lie algebroids
• A general framework for nonholonomic mechanics: Nonholonomic Systems on Lie affgebroids
• Dynamical Equations and Lagrange--Ricci Flow Evolution on Prolongation Lie Algebroids
• Linearization of nonlinear connections on vector and affine bundles, and some applications
• Exterior differential systems on Lie algebroids and the invariant inverse problem of the calculus of variations