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Lie algebroid structures and Lagrangian systems on affine bundles. (English) Zbl 1010.37032

Summary: 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.

MSC:

37J05 Relations of dynamical systems with symplectic geometry and topology (MSC2010)
53D17 Poisson manifolds; Poisson groupoids and algebroids
70G45 Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics
58H05 Pseudogroups and differentiable groupoids
70H03 Lagrange’s equations
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References:

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