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In this present communication the relativistic formulation of the curl forceswith saddle potentials has been performed. In particular, we formulated therelativistic version of the Kapitza equation. The dynamics and trappingphenomena of this equation have been studied both theoretically andnumerically. The numerical results show interesting characteristics of thecharged particles associated with the particle trapping and escaping in therelativistic domain. In addition, the relativistic generalization of theKapitza equation associated with the monkey saddle has also been discussed.

Relativistic formulation of curl force, relativistic Kapitza equation and trapping