http://swrc.ontoware.org/ontology#Article
Stability of vertical magnetic chains
en
Schönke Johannes
Fried Eliot
Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences
473
2198
2017-02-08
A linear stability analysis is performed for a pair of coaxial vertical chains made from permanently magnetized balls under the influence of gravity. While one chain rises from the ground, the other hangs from above, with the remaining ends separated by a gap of prescribed length. Various boundary conditions are considered, as are situations in which the magnetic dipole moments in the two chains are parallel or antiparallel. The case of a single chain attached to the ground is also discussed. The stability of the system is examined with respect to three quantities: the number of balls in each chain, the length of the gap between the chains, and a single dimensionless parameter which embodies the competition between magnetic and gravitational forces. Asymptotic scaling laws involving these parameters are provided. The Hessian matrix is computed in exact form, allowing the critical parameter values at which the system loses stability and the respective eigenmodes to be determined up to machine precision. A comparison with simple experiments for a single chain attached to the ground shows good agreement.
The Royal Society
1471-2946
info:pmid/28293135
info:doi/10.1098/rspa.2016.0703
© 2017 The Authors.
http://rspa.royalsocietypublishing.org/content/473/2198/20160703