Locating the sets of exceptional points in dissipative systems and the self-stability of bicycles

Kirillov, Oleg (2018) Locating the sets of exceptional points in dissipative systems and the self-stability of bicycles. Entropy, 20 (7). p. 502. ISSN 1099-4300

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Official URL: https://doi.org/10.3390/e20070502

Abstract

Sets in the parameter space corresponding to complex exceptional points have high codimension and by this reason they are difficult objects for numerical location. However, complex EPs play an important role in the problems of stability of dissipative systems where they are frequently considered as precursors to instability. We propose to locate the set of complex EPs using the fact that the global minimum of the spectral abscissa of a polynomial is attained at the EP of the highest possible order. Applying this approach to the problem of self-stabilization of a bicycle we find explicitly the EP sets that suggest scaling laws for the design of robust bikes that agree with the design of the known experimental machines.

Item Type: Article
Uncontrolled Keywords: exceptional points in classical systems; coupled systems; non-holonomic constraints; nonconservative forces; stability optimization; spectral abscissa; swallowtail; bicycle self-stability
Subjects: F300 Physics
H300 Mechanical Engineering
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: Paul Burns
Date Deposited: 28 Jun 2018 16:21
Last Modified: 15 Feb 2019 15:00
URI: http://nrl.northumbria.ac.uk/id/eprint/34750

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