Abstract
Abstract. We consider stability of solitons of the Maxwell–Lorentz system with extended charged spinning particle. The solitons are solutions which correspond to a particle moving with a constant velocity v with |v| < 1 and rotating with a constant angular velocity ω, [1]–[4]. Our main results are the orbital stability of moving solitons with ω = 0 and a linear orbital stability of rotating solitons with v = 0. The Hamilton–Poisson structure of the Maxwell–Lorentz system is degenerate and admits the Casimir invariants, [1]. We construct the Lyapunov function as a linear combination of the Hamiltonian with a suitable Casimir invariant. The key point is a lower bound for this function. The proof of the bound in the case ω ≠ 0 relies on angular momentum conservation and suitable spectral arguments including the Heinz inequality and closed graph theorem
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