Journal of Vcibration Testing and System Dynamics 3(2) (2019) 233--235 | DOI:10.5890/JVTSD.2019.06.005

Fotios Georgiades

School of Engineering, College of Science, University of Lincoln, Lincoln, UK

Abstract

The form of the lower part of the vector eld erroneously leads to the conclusion/statement that the original system in 1st order has no linear counterpart, which is untrue. In here, the decomposition to linear and nonlinear part of the 1st order original system it is shown. The eigenvalues of the matrix associated with the linear part are all zero, therefore it cannot be claimed Lyapunov's conclusion that the system in low energies can be approximated with the linear counterpart. Also, two typographic errors have been corrected. The corrections and the additions not only don't affect the value of the rest part of the published article but also enhance the value of the original manuscript. More precisely, since the original system in low energies cannot be approximated by the solution of the linear counterpart, the followed approach to describe the dynamics of the spinning shaft with linearization around the equilibria of the restricted system which are the rigid body motions, is of higher significance.

Acknowledgments

The author would like to thank Prof. Y. Mikhlin, in providing information about relevant literature to search for approximation of the original system in case that the linear counterpart has zero eigenvalues.

References

1. [1]	Mikhlin, Y.V. and Avramov, K.V. (2010), Nonlinear normal modes for vibrating mechanical systems. Review of Theoretical Developments, Applied Mechanics Reviews, 63 / 060802-1:21.

2. [2]	Malcolm, S. (1995), Book reviews: A.M. Luapunov, The General Problem of the Stability of Motion, Automatica, 31, pp353-356.

3. [3]	Perco, L. (1991), Differential Equarions and Dynamical Systems, Springer-Verlag.

4. [4]	Prof. Y. V. Mikhlin, 7 March 2019.