Stability of a flexible missile described by asymptotics of the eigenvalues of fourth order boundary value problems

2021/10/05 by Zinsou, Bertin
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2110.02306

Abstract

Fourth order problems, with the differential equation y⁽⁴⁾-(gy')'=λ²y, where g∈ C¹[0,a] and a>0, occur in engineering on stability of elastic rods. They occur as well in aeronautics to describe the stability of a flexible missile. Fourth order Birkhoff regular problems with the differential equation y⁽⁴⁾-(gy')'=λ²y and eigenvalue dependent boundary conditions are considered. These problems have quadratic operator representations with non self-adjoint operators. The first four terms of the asymptotics of the eigenvalues of the problems as well as those of the eigenvalues of the problem describing the stability of a flexible missile are evaluated explicitly.

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