Tulczyjew's Triplet for Lie Groups II: Dynamics

zbMath1404.53097arXiv1503.06566MaRDI QIDQ5269335

Hasan Gümral, Oğul Esen

Publication date: 15 June 2017

Full work available at URL: https://arxiv.org/abs/1503.06566

zbMATH Keywords

Lagrangian submanifoldEuler-Poincaré equationsLegendre transformationtrivialized Euler-Lagrange equationsdiffeomorphisms groupLie-Poisson equationsMorse familiesTulczyjew's triplettrivialized Hamilton's equations

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Hamilton's equations (70H05) Lie algebras of Lie groups (22E60) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Lagrange's equations (70H03) Averaging of perturbations for nonlinear problems in mechanics (70K65)

Related Items (10)

Lagrangian Lie subalgebroids generating dynamics for second-order mechanical systems on Lie algebroids ⋮ Hamiltonian dynamics on matched pairs ⋮ A Hamilton–Jacobi formalism for higher order implicit Lagrangians ⋮ Lagrangian dynamics on matched pairs ⋮ Tulczyjew’s triplet with an Ehresmann connection I: Trivialization and reduction ⋮ Tulczyjew’s triplet for lie groups III: Higher order dynamics and reductions for iterated bundles ⋮ Second order Lagrangian dynamics on double cross product groups ⋮ Matched pair analysis of the Vlasov plasma ⋮ On the geometry of the Schmidt-Legendre transformation ⋮ The Tulczyjew triple in mechanics on a Lie group

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