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Generalized Emden–Fowler equations related to constant curvature surfaces and noncentral curl forces

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Abstract

A noncentral force is a prototypical example of nonconservative position dependent force, known as curl force; this terminology was first proposed by Berry and Shukla in [1]. In this paper, we extend the construction of a noncentral force on the Euclidean plane to constant curvature spaces. It is known that the angular momentum is not conserved in a noncentral setting; we take angular momentum and integral torque to be two independent coordinates and study two different reductions of noncentral forces using these two new variables. These lead to the curvature-dependent generalized Emden–Fowler and generalized Lane–Emden equations. These reduce to the standard form of the Emden–Fowler and Lane–Emden equations when the curvature vanishes. We compute all the generalized Emden–Fowler equations based on polynomial noncentral forces. Finally, we also give a brief outline of our construction for nonpolynomial forces.

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Acknowledgements

I am immensely grateful to Professor Sir Michael Berry for his valuable remarks. I am also grateful to Haret Rosu for his suggestions and comments. I am also indebted to Professors Praghya Shukla, Stefan Mancas and Anindya Ghose–Choudhury for various discussions and correspondences.

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

    Partha Guha

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Guha, P. Generalized Emden–Fowler equations related to constant curvature surfaces and noncentral curl forces. Acta Mech 232, 3381–3391 (2021). https://doi.org/10.1007/s00707-021-02998-3

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