Lie algebroid structures and Lagrangian systems on affine bundles

DOI10.1016/S0393-0440(02)00114-6zbMath1010.37032arXivmath/0203178MaRDI QIDQ1864906

Tom Mestdag, Willy Sarlet, Eduardo Martínez

Publication date: 23 March 2003

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0203178

zbMATH Keywords

affine spacesLagrangian systemsLie algebroidprolongation

Mathematics Subject Classification ID

Related Items (24)

Symmetries of second order differential equations on Lie algebroids ⋮ Sub-Lagrangians and sub-Hamiltonians on affine bundles ⋮ Jacobi structures on affine bundles ⋮ AV-differential geometry and Newtonian mechanics ⋮ Generalised connections on affine Lie algebroids. ⋮ On the geometry of the Hamilton-Jacobi equation and generating functions ⋮ Higher-order variational calculus on Lie algebroids ⋮ Almost Kähler Ricci flows and Einstein and Lagrange-Finsler structures on Lie algebroids ⋮ Symmetries of Hamiltonian systems on Lie algebroids ⋮ Linearization of nonlinear connections on vector and affine bundles, and some applications ⋮ Jacobi groupoids and generalized Lie bialgebroids. ⋮ Classical field theory on Lie algebroids: multisymplectic formalism ⋮ General framework for nonholonomic mechanics: Nonholonomic systems on Lie affgebroids ⋮ AV-differential geometry: Euler-Lagrange equations ⋮ Vector hulls of affine spaces and affine bundles ⋮ GEOMETRIC ASPECTS OF TIME-DEPENDENT SINGULAR DIFFERENTIAL EQUATIONS ⋮ Lagrangian submanifolds and dynamics on Lie affgebroids ⋮ AV-differential geometry: Poisson and Jacobi structures ⋮ Dirac algebroids in Lagrangian and Hamiltonian mechanics ⋮ The Tulczyjew triple in mechanics on a Lie group ⋮ Variational calculus on Lie algebroids ⋮ ON SECOND NOETHER'S THEOREM AND GAUGE SYMMETRIES IN MECHANICS ⋮ A SURVEY OF LAGRANGIAN MECHANICS AND CONTROL ON LIE ALGEBROIDS AND GROUPOIDS ⋮ THE HAMILTON–JACOBI EQUATION ON LIE AFFGEBROIDS

Cites Work

• Algebraic constructions in the category of Lie algebroids
• Lie algebroids and Poisson-Nijenhuis structures
• Lie brackets on affine bundles
• Lie algebroids, holonomy and characteristic classes
• Some linear Jacobi structures on vector bundles
• Lie Algebroids and Lie Pseudoalgebras
• Tangent Lie algebroids
• On the geometry of Lie algebras and Poisson tensors
• Lagrangian mechanics on Lie algebroids
• Generalized Lie bialgebroids and Jacobi structures
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