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G. Gottwald and M. Oliver,
Slow dynamics via degenerate variational asymptotics,
Proc. R. Soc. Lond. A 470 (2014), 20140460,
doi:10.1098/rspa.2014.0460.
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.
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