Physics – Mathematical Physics
Scientific paper
2011-01-17
Physics
Mathematical Physics
Scientific paper
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 quasi-stationary 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 so-called relative equilibria [3], i.e. the trajectories of the system dynamics which are at the same time one-parameter subgroups of the system invariance group. Nowadays their stability is normally investigated using two similar approaches -- energy-momentum and energy-Casimir 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.
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