MATHEMATICAL MODELS OF PHYSICO-MECHANICAL SYSTEMS

Reality of frequencies of small disturbances for a string with a fixed end

M. A. Hanygin, G. S. Sharov

Tver State University, Tver

Abstract: For the open relativistic string with one massive end and one fixed end arbitrary small disturbances of uniform rotations are studied. There are two classes of these disturbances with different spectra of frequencies. They correspond to string oscillations in the rotational plane and in the orthogonal direction. Equations for spectra of small disturbances are deduced. It is shown that their roots (frequencies of small disturbances) are real simple roots. This fact confirms stability of string uniform rotations with respect to small disturbances.

Keywords: string with massive ends, small disturbances, stability, spectrum of frequencies.

UDC: 517.8

Received: 16.06.2009
Revised: 23.06.2009

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