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Using Lorentz force equation as an input a Hamiltonian mechanics on thenon-projective two twistor phase space TxT is formulated. Such a constructionautomatically reproduces dynamics of the intrinsic classical relativistic spin.The charge appears as a dynamical variable. It is also shown that if theclassical relativistic spin function on TxT vanishes, the natural conformallyinvariant symplectic structure on TxT reduces to the natural symplecticstructure on the cotangent bundle of the Kaluza-Klein space.

Twistor phase space dynamics and the Lorentz force equation