On the Stability of Solitons for the Maxwell-Lorentz Equations with Rotating Particle

Abstract We prove the stability of solitons Maxwell–Lorentz equations with extended charged rotating particle. The are solutions which correspond to uniform rotation To stability, we construct Hamilton–Poisson representation system. construction relies on Hamilton least action principle. constructed structure is degenerate and admits a functional family Casimir invariants. This allows us Lyapunov function corresponding soliton. combination Hamiltonian suitable invariant. conserved, soliton its critical point. key point proof lower bound for function. implies that strict local minimizer holds if effective moment inertia particle in Maxwell field sufficiently large respect “bar inertia".