Relativistic formulation of curl force, relativistic Kapitza equation and trapping

In this present communication the relativistic formulation of the curl forces with saddle potentials has been performed. In particular, we formulated the relativistic version of the Kapitza equation. The dynamics and trapping phenomena of this equation have been studied both theoretically and numerically. The numerical results show interesting characteristics of the charged particles associated with the particle trapping and escaping in the relativistic domain. In addition, the relativistic generalization of the Kapitza equation associated with the monkey saddle has also been discussed. PACS numbers: 05.45.-a, 45.20.-d, 45.20.Dd, 45.50.Jf 2020 Mathematics Subject Classification: 01A75, 34A05, 70J25, 70H14

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