Vibrations of a horizontal elastic shaft with a fixed heavy disk on it is described by a system of three nonlinear differential equations of the second order. A. Stodola suggested a particular solution of this system which corresponds to the second critical speed, but a purely theoretical analysis, of the stability of the particular solution suggested by A. Stodola has not been carried out.
An attempt to find a solution of this problem is made in this article. In his analysis the writer uses the method of calculating the logarithm of the monodromy matrix suggested by , [7, a], .
In our case it enabled us
a)to state the necessary and sufficient conditions of stability,
b)to calculate the zone of stability in the space of parameters.
Citation Example:Zatepiakin M. M. On the theory of critical speeds of rotatings hafts // Ukr. Mat. Zh. - 1961. - 13, № 2. - pp. 142-149.