Two-timing, variational principles and waves
- Creators
- Whitham, G. B.
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.
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.Attached Files
Published - WHIjfm70.pdf
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Additional details
- Eprint ID
- 33043
- Resolver ID
- CaltechAUTHORS:20120809-093816811
- Office of Naval Research (ONR)
- Created
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2012-08-09Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field