Brouwer's problem on a heavy particle in a rotating vessel: wave propagation, ion traps, and rotor dynamics

Details Brouwer's problem on a heavy particle in a rotating vessel: wave propagation, ion traps, and rotor dynamics Brouwer's problem on a heavy particle in a rotating vessel: wave propagation, ion traps, and rotor dynamics

2010-12-04

arxiv.org/abs/1012.0892v1

Physics Letters A 375 (2011) 1653-1660

Physics

Mathematical Physics

18 pages, 6 figures

Scientific paper

10.1016/j.physleta.2011.02.056

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 Brouwer's 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.

Affiliated with

Also associated with

No associations

Rating

Brouwer's problem on a heavy particle in a rotating vessel: wave propagation, ion traps, and rotor dynamics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Brouwer's problem on a heavy particle in a rotating vessel: wave propagation, ion traps, and rotor dynamics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Brouwer's problem on a heavy particle in a rotating vessel: wave propagation, ion traps, and rotor dynamics will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-99232