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Relativistic formulation of curl force, relativistic Kapitza equation and trapping

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Abstract

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.

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Acknowledgements

PG is immensely grateful to Professor Sir Michael Berry for his critical and meticulous reading of this draft and for making invaluable remarks and or comments. PG and SG also convey their sincere thanks to Professor Haret Rosu for his suggestions and comments and Professors Praghya Shukla, Stefan Mancas and Anindya Ghose-Choudhury for various discussions and correspondences. PG thanks Khalifa University of Science and Technology for its continued support toward this research work under the grant number FSU-2021-014 and SG thanks Diamond Harbour Women’s University for providing the necessary research environment with constant encouragement and support. Lastly, the authors are grateful to the anonymous referees for their constructive comments in connection with the betterment of the manuscript.

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Authors and Affiliations

  1. Department of Physics, Diamond Harbour Women’s University, D. H. Road, Sarisha, West-Bengal, 743368, India

    Sudip Garai

  2. Department of Mathematics, Khalifa University of Science and Technology, Main Campus, P.O. Box -127788, Abu Dhabi, UAE

    Partha Guha

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  1. Partha Guha
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Guha, P., Garai, S. Relativistic formulation of curl force, relativistic Kapitza equation and trapping. Nonlinear Dyn 111, 9863–9874 (2023). https://doi.org/10.1007/s11071-023-08385-y

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