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Generalized Emden–Fowler equations related to constant curvature surfaces and noncentral curl forces
Acta Mechanica ( IF 2.7 ) Pub Date : 2021-06-22 , DOI: 10.1007/s00707-021-02998-3
Partha Guha

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.



中文翻译:

与等曲率曲面和非中心卷曲力相关的广义 Emden-Fowler 方程

非中心力是非保守的位置相关力的典型例子,称为卷曲力;该术语最早由 Berry 和 Shukla 在 [1] 中提出。在本文中,我们将欧几里得平面上的非中心力的构造扩展到恒定曲率空间。众所周知,角动量在非中心环境中不守恒;我们将角动量和积分扭矩作为两个独立的坐标,并使用这两个新变量研究非中心力的两种不同减少。这些导致曲率相关的广义 Emden-Fowler 和广义 Lane-Emden 方程。当曲率消失时,这些方程简化为 Emden-Fowler 和 Lane-Emden 方程的标准形式。我们计算所有基于多项式非中心力的广义 Emden-Fowler 方程。最后,

更新日期:2021-06-22
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