Slow dynamics via degenerate variational asymptotics

Abstract

We introduce the method of degenerate variational asymptotics for a class of singularly perturbed ordinary differential equations in the limit of strong gyroscopic forces. Such systems exhibit dynamics on two separate time scales. We derive approximate equations for the slow motion to arbitrary order through an asymptotic expansion of the Lagrangian in suitably transformed coordinates. We prove that the necessary near-identity change of variables can always be constructed and that solutions of the slow limit equations shadow solutions of the full parent model at the expected order over a finite interval of time.

Locations

• Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences - View - PDF
• CiteSeer X (The Pennsylvania State University) - View - PDF