Abstract In this paper we present some relevant dynamical properties of an idealized conservative model of the rattleback, from the Poisson dynamics point of view. In the first half of the article, along with a dynamical study of the orbits, using a Hamilton–Poisson realization of the dynamical system, we provide a geometric characterization of the space of orbits in terms of Whitney stratifications associated to the image of the energy–Casimir mapping. In the second half of the article we provide an explicit method to stabilize asymptotically any arbitrary fixed orbit/cycle of the rattleback system and to keep unchanged the geometry of the model space.

中文翻译：

---

关于响尾蛇动力学

摘要 在本文中，我们从泊松动力学的角度介绍了响尾蛇理想化保守模型的一些相关动力学特性。在文章的前半部分，连同对轨道的动力学研究，使用动力学系统的 Hamilton-Poisson 实现，我们根据与能量图像相关的惠特尼分层提供了轨道空间的几何特征–卡西米尔映射。在文章的后半部分，我们提供了一种明确的方法来渐近稳定响尾蛇系统的任何任意固定轨道/周期，并保持模型空间的几何形状不变。