# Stability of Hamiltonian relative equilibria in symmetric magnetically confined rigid bodies

This work studies the symmetries, the associated momentum map, and relative equilibria of a mechanical system consisting of a small axisymmetric magnetic body-dipole in an also axisymmetric external magnetic field that additionally exhibits a mirror symmetry; we call this system the ``orbitron". We study the nonlinear stability of a branch of equatorial quasiorbital relative equilibria using the energy-momentum method and we provide sufficient conditions for their $\mathbb{T}^{2}$