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Generalized Emden–Fowler equations in noncentral curl forces and first integrals

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Abstract

Noncentral force is an exemplary example of curl force and in general this is not an integrable system. The purpose of this note is twofold. First, we study a different reduction in the noncentral force compared to Berry and Shukla, and this leads to the generalized Emden–Fowler (GEF) equation, which in turn can be mapped to the Thomas–Fermi equation. Second, we compute the first integrals of the integrable standard Emden–Fowler (EF) and the generalized EF equations associated with the reduced noncentral dynamics using old results and new techniques. Finally, we compute the reduction in the nonpolynomial noncentral forces, which also leads to generalized EF equations.

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Acknowledgements

I am immensely grateful to Professor Sir Michael Berry, since this note arose from the discussion with him when he was visiting IACS Kolkata in March 2019. I am grateful to Professor Satrajit Adhikari for his kind hospitality at IACS. I am also indebted to Professors Praghya Shukla, Thanu Padmanabhan, Haret Rosu and Anindya Ghose-Choudhury for various discussions and correspondences. Finally, I would like to thank the two anonymous reviewers for their suggestions and comments.

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  1. SN Bose National Centre for Basic Sciences, JD Block, Sector III, Salt Lake, Kolkata, 700098, India

    Partha Guha

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Correspondence to Partha Guha.

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Guha, P. Generalized Emden–Fowler equations in noncentral curl forces and first integrals. Acta Mech 231, 815–825 (2020). https://doi.org/10.1007/s00707-019-02602-9

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  • DOI: https://doi.org/10.1007/s00707-019-02602-9

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