Variational calculus on Lie algebroids

DOI10.1051/cocv:2007056zbMath1135.49027arXivmath-ph/0603028OpenAlexW2145108423MaRDI QIDQ5458124

Eduardo Martínez

Publication date: 11 April 2008

Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0603028

zbMATH Keywords

variational calculusLie algebroidsEuler-Poincaré equationsLagrangian mechanicsLagrange-Poincaré equationsreduction of dynamical systems

Mathematics Subject Classification ID

Lie algebras of vector fields and related (super) algebras (17B66) Hamilton's principle (70H25) Topological groupoids (including differentiable and Lie groupoids) (22A22) Optimality conditions for problems involving ordinary differential equations (49K15) Manifolds of mappings (58D15) Variational principles of physics (49S05)

Related Items (17)

Second-order constrained variational problems on Lie algebroids: applications to optimal control ⋮ Second-order variational problems on Lie groupoids and optimal control applications ⋮ On the geometry of the Hamilton-Jacobi equation and generating functions ⋮ Higher-order variational calculus on Lie algebroids ⋮ Euler-Lagrange-Herglotz equations on Lie algebroids ⋮ Classical field theory on Lie algebroids: multisymplectic formalism ⋮ Banach-Lie groupoids and generalized inversion ⋮ Singular Lagrangian systems and variational constrained mechanics on Lie algebroids ⋮ Lagrangian mechanics and reduction on fibered manifolds ⋮ Higher-order analogs of Lie algebroids via vector bundle comorphisms ⋮ The Tulczyjew triple in mechanics on a Lie group ⋮ An extension of the Dirac and Gotay-Nester theories of constraints for Dirac dynamical systems ⋮ Models for higher algebroids ⋮ Local convexity for second order differential equations on a Lie algebroid ⋮ Nonholonomic constraints: A new viewpoint ⋮ A comparison of vakonomic and nonholonomic dynamics with applications to non-invariant Chaplygin systems ⋮ Jacobi fields for second-order differential equations on Lie algebroids

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