The anatylical mechanics representations of a charged particle moving in a uniform magnetic field with radiation friction are studied. First, by solving the inverse problem of Birkhoffian mechanics for the differential equations of motion the 4 Birkhoffian representations of the charged particle are obtained. Secondly, 4 Lagrangian representations in the state space and 4 Lagrangian representations in the configuration space are derived, and then 4 Hamiltonians are constructed. Lastly, 4 first integrals are obtained from the analytical mechanics representations of the moving particle, and the solutions of the equations of motion are presented.