Research into Orbital Motion Stability in System of Two Magnetically Interacting Bodies
Abstract
The stability of the orbital motion of two long cylindrical magnets interacting exclusively with magnetic forces is described. To carry out analytical studies a model of magnetically interacting symmetric tops [1] is used. The model was previously developed within the quasistationary approach for an electromagnetic field based on the general expression of the energy of interacting magnetic bodies [2]. A special role in the investigation of the stability of orbital motions is played by the socalled relative equilibria [3], i.e. the trajectories of the system dynamics which are at the same time oneparameter subgroups of the system invariance group. Nowadays their stability is normally investigated using two similar approaches  energymomentum and energyCasimir methods. The most suitable criterion for the system stability investigation was formulated in the theorem of [4]; this stability criterion successfully generalizes both the methods mentioned above and covers the Hamiltonian formalism based on Poisson structures [1]. The necessary and sufficient conditions for the circular orbit stability are derived from this theorem.
 Publication:

arXiv eprints
 Pub Date:
 January 2011
 DOI:
 10.48550/arXiv.1101.3237
 arXiv:
 arXiv:1101.3237
 Bibcode:
 2011arXiv1101.3237Z
 Keywords:

 Mathematical Physics