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We consider Dirichlet Laplacian in a thin curved three-dimensional rod. Therod is finite. Its cross-section is constant and small, and rotates along thereference curve in an arbitrary way. We find a two-parametric set of theeigenvalues of such operator and construct their complete asymptoticexpansions. We show that this two-parametric set contains any prescribed numberof the first eigenvalues of the considered operator. We obtain the completeasymptotic expansions for the eigenfunctions associated with these firsteigenvalues.

Complete asymptotic expansions for eigenvalues of Dirichlet Laplacian in thin three-dimensional rods