2020/11/11 by Richard Beals, Beals, Richard, Jacek Szmigielski +1 · 2 citations
Chemistry · Materials Science · Physics and Astronomy · #35Q51 #Classical Analysis and ODEs (math.CA) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Molecular spectroscopy and chirality #Nonlinear Optical Materials Research #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2011.05964
openalex publication_date 2020/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A new approach to the Euler-Bernoulli beam based on an inhomogeneous matrix string problem is presented. Three ramifications of the approach are developed: (1) motivated by an analogy with the Camassa-Holm equation a class of isospectral deformations of the beam problem is formulated; (2) a reformulation of the matrix string problem in terms of a certain compact operator is used to obtain basic spectral properties of the inhomogeneous matrix string problem with Dirichlet boundary conditions; (3) the inverse problem is solved for the special case of a discrete Euler-Bernoulli beam. The solution involves a non-commutative generalization of Stieltjes' continued fractions, leading to the inverse formulas expressed in terms of ratios of Hankel-like determinants.