On the Lagrangian theory for rotating charge in the Maxwell field

• We study rotating charged particle in Maxwell electromagnetic field.
• We derive non-relativistic Abraham equation from Hamilton least action principle.
• For proof we apply variational Poincaré equations on the Lie group SO(3)SO(3).

We justify the Hamilton least action principle for the Maxwell–Lorentz equations coupled with the equations of motion of Abraham's rotating extended electron. The main novelty in the proof is the application of the variational Poincaré equations on the Lie group SO(3)SO(3).