Un-Reduction of Systems of Second-Order Ordinary Differential Equations

Abstract

In this paper we consider an alternative approach to "un-reduction". This is the process where one associates to a Lagrangian system on a manifold a dynamical system on a principal bundle over that manifold, in such a way that solutions project. We show that, when written in terms of second-order ordinary differential equations (SODEs), one may associate to the first system a (what we have called) "primary un-reduced SODE", and we explain how all other un-reduced SODEs relate to it. We give examples that show that the considered procedure exceeds the realm of Lagrangian systems and that relate our results to those in the literature.

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• An overview of the Riemannian metrics on spaces of curves using the Hamiltonian approach
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Cited by in corpus (1)

• Nonlinear splittings on fibre bundles