In this paper, we classify irreducible Darboux polynomials and rational first integrals of the nonstretching Rolie–Poly model by a new method based on the classical characteristic curves method. The classical method has been successfully applied to many systems, but it is not suitable for the nonstretching Rolie–Poly model. We take it as an auxiliary tool to give a preliminary understanding of the structure of the Darboux polynomials, and obtain partial integrability results of the system.

中文翻译：

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Darboux多项式和非拉伸Rolie–Poly模型的有理第一积分

在本文中，我们通过一种基于经典特征曲线方法的新方法，对不可拉伸的Darboux多项式和非拉伸Rolie–Poly模型的有理第一积分进行分类。经典方法已成功应用于许多系统，但不适用于非拉伸Rolie–Poly模型。我们将其作为辅助工具来初步了解Darboux多项式的结构，并获得系统的部分可积结果。