Various applications are described in the literature (10-12) where periodic perturbation
or symmetry breaking is introduced to cause chaotic particle trajectories in the deterministic flow patterns.
The interface of the guiding and metal layers has given a periodic perturbation
similar to grating structure.
The classical approach to the problem uses convex analysis (Rockafellar, 1970) to derive first-order conditions for improvement around an a priori known steady-state solution to the optimization problem using periodic perturbation
Laplace's periodic perturbation
and the secular tidal interaction both dwarf the orbital energy loss we now attribute to general relativity.
The periodically inserted B zone (no-barrier zone) is regarded as the periodic perturbation
in our modeling.
But because the comet--and the meteoroid stream all along its orbit--have made hundreds of trips around the Sun over tens of thousands of years, slight periodic perturbations
can add up.
Its influence upon the satellite orbit is illuminated by Kozai, and the periodic perturbations
of the first order and secular perturbations up to the second order are derived.