Brouwerʼs problem on a heavy particle in a rotating vessel: Wave propagation, ion traps, and rotor dynamics

Kirillov, Oleg (2011) Brouwerʼs problem on a heavy particle in a rotating vessel: Wave propagation, ion traps, and rotor dynamics. Physics Letters A, 375 (15). pp. 1653-1660. ISSN 0375-9601

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Abstract

In 1918 Brouwer considered stability of a heavy particle in a rotating vessel. This was the first demonstration of a rotating saddle trap which is a mechanical analogue for quadrupole particle traps of Penning and Paul. We revisit this pioneering work in order to uncover its intriguing connections with classical rotor dynamics and fluid dynamics, stability theory of Hamiltonian and non-conservative systems as well as with the modern works on crystal optics and atomic physics. In particular, we find that the boundary of the stability domain of the undamped Brouwerʼs problem possesses the Swallowtail singularity corresponding to the quadruple zero eigenvalue. In the presence of dissipative and non-conservative positional forces there is a couple of Whitney umbrellas on the boundary of the asymptotic stability domain. The handles of the umbrellas form a set where all eigenvalues of the system are pure imaginary despite the presence of dissipative and non-conservative positional forces.

Item Type:	Article
Uncontrolled Keywords:	rotating saddle, dissipation-induced instabilities, Merkin theorem, Swallowtail, Whitney umbrella, exceptional point
Subjects:	F300 Physics G100 Mathematics H300 Mechanical Engineering
Department:	Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User:	Oleg Kirillov
Date Deposited:	23 Jan 2017 13:11
Last Modified:	12 Oct 2019 22:27
URI:	http://nrl.northumbria.ac.uk/id/eprint/29278

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