Lagrangian submanifolds and dynamics on Lie affgebroids

DOI10.1016/S0034-4877(06)80029-7zbMath1143.53073arXivmath/0505117MaRDI QIDQ2480642

Diana Sosa, David Iglesias, Juan Carlos Marrero, Edith Padrón

Publication date: 3 April 2008

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0505117

zbMATH Keywords

Euler-Lagrange equationsHamilton equationscanonical involutionTulczyjew's tripleLie affgebroidsAtiyah affgebroidsLagrangian sunmanifoldssympletic Lie affgebroidstime-dependent mechanics

Mathematics Subject Classification ID

Lie algebras of vector fields and related (super) algebras (17B66) Hamilton's equations (70H05) Lagrangian submanifolds; Maslov index (53D12) Hamilton-Jacobi equations in mechanics (70H20) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Lagrange's equations (70H03)

Related Items (8)

AV-differential geometry and Newtonian mechanics ⋮ Lagrangian submanifolds and the Hamilton-Jacobi equation ⋮ Tulczyjew’s triplet with an Ehresmann connection I: Trivialization and reduction ⋮ Classical field theory on Lie algebroids: multisymplectic formalism ⋮ General framework for nonholonomic mechanics: Nonholonomic systems on Lie affgebroids ⋮ AV-differential geometry: Euler-Lagrange equations ⋮ Affine Hamiltonians in higher order geometry ⋮ Dirac algebroids in Lagrangian and Hamiltonian mechanics

Cites Work

• AV-differential geometry: Poisson and Jacobi structures
• Algebraic constructions in the category of Lie algebroids
• Lie bialgebroids and Poisson groupoids
• Tangent and cotangent lifts and graded Lie algebras associated with Lie algebroids
• Lie algebroids and Poisson-Nijenhuis structures
• Lie brackets on affine bundles
• Lie algebroid structures and Lagrangian systems on affine bundles
• Lagrangian reduction by stages
• Lie algebroid structures on a class of affine bundles
• Lagrangian submanifolds and dynamics on Lie algebroids
• Lagrangian mechanics on Lie algebroids
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