Routh’s procedure for non-Abelian symmetry groups

DOI10.1063/1.2885077zbMath1153.37396arXiv0802.0528OpenAlexW2064139848MaRDI QIDQ3544667

Mike Crampin, Tom Mestdag

Publication date: 8 December 2008

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0802.0528

Mathematics Subject Classification ID

Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) (n)-body problems (70F10) Lagrange's equations (70H03)

Related Items (18)

Implicit Lagrange-Routh equations and Dirac reduction ⋮ Finsler geodesics of Lagrangian systems through Routh reduction ⋮ Variational problems with symmetries: a Pfaffian system approach ⋮ Routh reduction of Palatini gravity in vacuum ⋮ A variational setting for an indefinite Lagrangian with an affine Noether charge ⋮ A note on hybrid Routh reduction for time-dependent Lagrangian systems ⋮ Relative equilibria of Lagrangian systems with symmetry ⋮ Routh reduction and Cartan mechanics ⋮ Anholonomic frames in constrained dynamics ⋮ The symmetry reduction of variational integrals ⋮ On the Lie integrability theorem for the Chaplygin ball ⋮ Aspects of reduction and transformation of Lagrangian systems with symmetry ⋮ Un-reduction of systems of second-order ordinary differential equations ⋮ Nonlinear splittings on fibre bundles ⋮ Geometry of Routh reduction ⋮ Routhian reduction for quasi-invariant Lagrangians ⋮ Routh reduction and the class of magnetic Lagrangian systems ⋮ Cotangent bundle reduction and Routh reduction for polysymplectic manifolds

Cites Work

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• Canonical formulations of a classical particle in a Yang-Mills field and Wong's equations
• Lagrangian reduction and the double spherical pendulum
• Stability of relative equilibria. I: The reduced energy-momentum method
• Reduction and reconstruction aspects of second-order dynamical systems with symmetry
• Reduction theory and the Lagrange–Routh equations
• Reduction, symmetry, and phases in mechanics
• Reduction of Hamilton's variational principle

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