Application of the Sonin-Pólya oscillation theorem
The necessary conditions for the Sonin-Polya theorem, which predicts the variation of the successive relative maxima of the oscillating solutions of a secondorder 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-Polya 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.