Research Papers

Stability of Gyroscopic Circulatory Systems

[+] Author and Article Information
Firdaus E. Udwadia

Aerospace and Mechanical Engineering,
Civil Engineering, Information and Operations
Management, and Mathematics,
430K Olin Hall,
University of Southern California,
Los Angeles, CA 90089-1453
e-mail: feuUSC@gmail.com

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received August 26, 2018; final manuscript received October 24, 2018; published online November 16, 2018. Assoc. Editor: George Haller.

J. Appl. Mech 86(2), 021002 (Nov 16, 2018) (6 pages) Paper No: JAM-18-1495; doi: 10.1115/1.4041825 History: Received August 26, 2018; Revised October 24, 2018

This paper presents results related to the stability of gyroscopic systems in the presence of circulatory forces. It is shown that when the potential, gyroscopic, and circulatory matrices commute, the system is unstable. This central result is shown to be a generalization of that obtained by Lakhadanov, which was restricted to potential systems all of whose frequencies of vibration are identical. The generalization is useful in stability analysis of large scale multidegree-of-freedom real life systems, which rarely have all their frequencies identical, thereby expanding the compass of applicability of stability results for such systems. Comparisons with results in the literature on the stability of such systems are made, and the weakness of results that deal with only general statements about stability is exposed. It is shown that the commutation conditions given herein provide definitive stability results in situations where the well-known Bottema–Karapetyan–Lakhadanov result is inapplicable.

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