Un-reduction of systems of second-order ordinary differential equations

DOI10.3842/SIGMA.2016.115zbMath1353.37115arXiv1606.07649OpenAlexW2468452476MaRDI QIDQ2520131

Eduardo García-Toraño Andrés, Tom Mestdag

Publication date: 13 December 2016

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.07649

zbMATH Keywords

symmetryreductionprincipal connectionLagrangian system

Mathematics Subject Classification ID

Geometric methods in ordinary differential equations (34A26) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33) Symmetries, Lie group and Lie algebra methods for problems in mechanics (70G65)

Related Items (1)

Nonlinear splittings on fibre bundles

Cites Work

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• Un-reduction
• Un-reduction in field theory
• Geodesic boundary value problems with symmetry
• Variational connections on Lie groups
• Generalized submersiveness of second-order ordinary differential equations
• Overview of the geometries of shape spaces and diffeomorphism groups
• Connections on tangent bundles
• Lagrangian reduction by stages
• Invariant Lagrangians, mechanical connections and the Lagrange–Poincaré equations
• Routh’s procedure for non-Abelian symmetry groups
• Submersive second order ordinary differential equations
• Lagrangian submanifolds and dynamics on Lie algebroids
• Invariant Affine Connections on Homogeneous Spaces

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