Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Application of the Sonin-Pólya oscillation theorem

Authors: E. V. Laitone and Wen Fan Lin
Journal: Quart. Appl. Math. 32 (1974), 285-291
MSC: Primary 33A30
DOI: https://doi.org/10.1090/qam/430343
MathSciNet review: 430343
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Abstract: The necessary conditions for the Sonin-Pólya theorem, which predicts the variation of the successive relative maxima of the oscillating solutions of a second-order ordinary differential equation, are evaluated for the confluent hypergeometric functions to prove that the criteria for their decreasing sequence, as given in [1], [2] and [3], are incorrect. The Sonin-Pólya theorem is then applied to the differential equation for the linearized shallow-water edge wave that is produced by a beach of constant slope. The final application is to Allen's differential equation for the angle of attack oscillations of a re-entry ballistic missile, and new stability criteria are obtained for both ascending and descending missiles that are coasting through the atmosphere.

References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/qam/430343
Article copyright: © Copyright 1974 American Mathematical Society

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