Abstract
A method is proposed for calculation of the complex eigenvalues of a boundary-value problem that describes the rotation of a long vertical partially compressed rod subject to the action of dead weight and torque. The solution of the problem is sought for two sections of the rod in the form of asymptotic expansions in a small parameter, which are then joined at a certain point. The results obtained are discussed and compared with the results of other studies. The method may be used for analysis of the rotation of a long vertical pipe in deep-well drilling.
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