2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/205082We solve exactly the classical non-relativistic Landau-Lifshitz equations of motion for a charged particle moving in a Coulomb potential, including radiation damping. The general solution involves the Painleve transcendent of type II. It confirms our physical intuition that a negatively charged classical particle will spiral into the nucleus, supporting the the validity of the Landau-Lifshitz equation.2 figures; Figure added, also minor comments and correctionsHigh Energy Physics - TheoryAstrophysicsMathematical PhysicsDynamical SystemsExactly Solvable and Integrable SystemsPlasma Physicstext