Routh Reduction by Stages

Abstract

This paper deals with the Lagrangian analogue of symplectic or point reduction by stages. We develop Routh reduction as a reduction technique that preserves the Lagrangian nature of the dynamics. To do so we heavily rely on the relation between Routh reduction and cotangent symplectic reduction. The main results in this paper are: (i) we develop a class of so called magnetic Lagrangian systems and this class has the property that it is closed under Routh reduction; (ii) we construct a transformation relating the magnetic Lagrangian system obtained after two subsequent Routh reductions and the magnetic Lagrangian system obtained after Routh reduction w.r.t. to the full symmetry group.

References in corpus (3)

• Routh's procedure for non-Abelian symmetry groups
• Routhian reduction for quasi-invariant Lagrangians
• The Dynamics of a Rigid Body in Potential Flow with Circulation

Cited by in corpus (7)

• Reduced dynamics and Lagrangian submanifolds of symplectic manifolds
• Routh reduction and the class of magnetic Lagrangian systems
• Aspects of reduction and transformation of Lagrangian systems with symmetry
• Nonlinear splittings on fibre bundles
• Hybrid Routhian reduction for simple hybrid forced Lagrangian systems
• Generalized hybrid momentum maps and reduction by symmetries of forced mechanical systems with inelastic collisions
• Cotangent bundle reduction and Routh reduction for polysymplectic manifolds