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A new approach to the Euler-Bernoulli beam based on an inhomogeneous matrixstring problem is presented. Three ramifications of the approach are developed:(1) motivated by an analogy with the Camassa-Holm equation a class ofisospectral deformations of the beam problem is formulated; (2) a reformulationof the matrix string problem in terms of a certain compact operator is used toobtain basic spectral properties of the inhomogeneous matrix string problemwith Dirichlet boundary conditions; (3) the inverse problem is solved for thespecial case of a discrete Euler-Bernoulli beam. The solution involves anon-commutative generalization of Stieltjes' continued fractions, leading tothe inverse formulas expressed in terms of ratios of Hankel-like determinants.

A 2-component Camassa-Holm equation, Euler-Bernoulli Beam Problem and Non-Commutative Continued Fractions