Discrete Lagrangian and Hamiltonian mechanics on Lie groupoids

DOI10.1088/0951-7715/19/6/006zbMath1162.17312arXivmath/0506299OpenAlexW2019151447MaRDI QIDQ5488811

Eduardo Martínez, David Martín de Diego, Juan Carlos Marrero

Publication date: 25 September 2006

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0506299

Mathematics Subject Classification ID

Related Items (31)

Euler-Poincaré reduction for discrete field theories ⋮ Discrete Hamilton–Jacobi theory for systems with external forces ⋮ The variational discretization of the constrained higher-order Lagrange-Poincaré equations ⋮ Variational order for forced Lagrangian systems ⋮ Exact discrete Lagrangian mechanics for nonholonomic mechanics ⋮ Variational integrators for mechanical control systems with symmetries ⋮ Second-order variational problems on Lie groupoids and optimal control applications ⋮ The Local Description of Discrete Mechanics ⋮ Discrete variational optimal control ⋮ Lagrangian dynamics on matched pairs ⋮ Discrete Lagrangian field theories on Lie groupoids ⋮ The inverse problem of the calculus of variations for discrete systems ⋮ On the geometry of the Hamilton-Jacobi equation and generating functions ⋮ Discrete connections on principal bundles: the discrete Atiyah sequence ⋮ Nonassociative analogs of Lie groupoids ⋮ Retraction maps: a seed of geometric integrators ⋮ A historical review on nonholomic mechanics ⋮ Discrete dynamical systems over double cross-product Lie groupoids ⋮ Discrete Dirac reduction of implicit Lagrangian systems with abelian symmetry groups ⋮ Variational order for forced Lagrangian systems II. Euler–Poincaré equations with forcing ⋮ Discrete mechanics on unitary octonions ⋮ Variational and geometric structures of discrete Dirac mechanics ⋮ Symplectic groupoids and discrete constrained Lagrangian mechanics ⋮ Generalized variational calculus for continuous and discrete mechanical systems ⋮ DISCRETE SECOND-ORDER EULER–POINCARÉ EQUATIONS: APPLICATIONS TO OPTIMAL CONTROL ⋮ Discrete nonholonomic Lagrangian systems on Lie groupoids ⋮ Lagrangian mechanics and reduction on fibered manifolds ⋮ Fluid-structure interaction in the Lagrange-Poincaré formalism: the Navier-Stokes and inviscid regimes ⋮ Lagrangian reduction of nonholonomic discrete mechanical systems by stages ⋮ Local convexity for second order differential equations on a Lie algebroid ⋮ Lagrangian reduction of discrete mechanical systems by stages

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