Geometry and physics of averaging with applications
type: Item
instance of: scholarly article
title: Geometry and physics of averaging with applications
zbMATH Open document ID: 0936.37040
DOI: 10.1016/S0167-2789(99)00022-6
author: Mark Levi
published in: Physica D
publication date: 2000-05-22T00:00:00Z
review text: The paper contains a new observation on the well-studied problem of Hamiltonian systems with rapid time-dependence. The author notes that behind the standard averaging procedure there lies some simple geometry. In particular, the averaged forces in a rapidly forced system are the constraint forces of an associated auxiliary nonholonomic system and the curvature of these constraints enter the expression for the averaged system. This paper gives a new insight into the method of confinement of charged particles such as the Paul trap. A very simple physical explanation of stability of the inverted pendulum with vertically vibrating suspension is presented.
Mathematics Subject Classification ID: 37J60
Mathematics Subject Classification ID: 37J05
Mathematics Subject Classification ID: 37J40
Mathematics Subject Classification ID: 34C29
Mathematics Subject Classification ID: 70H45
zbMATH DE Number: 1370244
zbMATH Keywords: averaging method
zbMATH Keywords: rapidly forced systems
zbMATH Keywords: Hamiltonian systems
zbMATH Keywords: rapidly time-dependence
zbMATH Keywords: averaging procedure
zbMATH Keywords: nonholonomic system
MaRDI profile type: Publication
cites work: Q5848809
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description: scientific article; zbMATH DE number 1370244