2011/01/17 by С. Зуб, Stanislav Zub, Zub, Stanislav
Engineering · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Geophysics and Sensor Technology #Mathematical Physics (math-ph) #Quantum and Classical Electrodynamics #Relativity and Gravitational Theory #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1101.3237
arxiv created 2011/01/17 · openalex publication_date 2011/01/17 · arxiv updated 2011/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.