Reduction and reconstruction aspects of second-order dynamical systems with symmetry

Abstract

We examine the reduction process of a system of second-order ordinary differential equations which is invariant under a Lie group action. With the aid of connection theory, we explain why the associated vector field decomposes in three parts and we show how the integral curves of the original system can be reconstructed from the reduced dynamics. An illustrative example confirms the results.

28 pages, to appear in Acta Appl. Math

References in corpus (1)

• Lagrangian submanifolds and dynamics on Lie algebroids

Cited by in corpus (9)

• Routh's procedure for non-Abelian symmetry groups
• Anholonomic frames in constrained dynamics
• Relative equilibria of Lagrangian systems with symmetry
• Geodesic Reduction via Frame Bundle Geometry
• Symmetry reduction, integrability and reconstruction in k-symplectic field theory
• Reduction of invariant constrained systems using anholonomic frames
• Geodesic extensions of mechanical systems with nonholonomic constraints
• Un-Reduction of Systems of Second-Order Ordinary Differential Equations
• Exterior differential systems on Lie algebroids and the invariant inverse problem of the calculus of variations