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Two-timing, variational principles and waves

Whitham, G. B. (1970) Two-timing, variational principles and waves. Journal of Fluid Mechanics, 44 (2). pp. 373-395. ISSN 0022-1120. http://resolver.caltech.edu/CaltechAUTHORS:20120809-093816811

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Abstract

In this paper, it is shown how the author's general theory of slowly varying wave trains may be derived as the first term in a formal perturbation expansion. In its most effective form, the perturbation procedure is applied directly to the governing variational principle and an averaged variational principle is established directly. This novel use of a perturbation method may have value outside the class of wave problems considered here. Various useful manipulations of the average Lagrangian are shown to be similar to the transformations leading to Hamilton's equations in mechanics. The methods developed here for waves may also be used on the older problems of adiabatic invariants in mechanics, and they provide a different treatment; the typical problem of central orbits is included in the examples.


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http://dx.doi.org/10.1017/S002211207000188X DOIUNSPECIFIED
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=383484&fulltextType=RA&fileId=S002211207000188XPublisherUNSPECIFIED
Additional Information:© 1970 Cambridge University Press. Received January 10 1970. Published Online March 29 2006. This research was supported by the Office of Naval Research, U.S. Navy.
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Office of Naval Research (ONR)UNSPECIFIED
Record Number:CaltechAUTHORS:20120809-093816811
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20120809-093816811
Official Citation: G. B. Whitham (1970). Two-timing, variational principles and waves. Journal of Fluid Mechanics, 44 , pp 373-395 doi:10.1017/S002211207000188X
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:33043
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:09 Aug 2012 17:41
Last Modified:26 Dec 2012 15:54

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