论文标题
部分可观测时空混沌系统的无模型预测
Symplectic Integrators in Corotating Coordinates
论文作者
论文摘要
旋转坐标中质量点的动态方程还受科里奥利和离心力的控制，除了相对于框架的脉冲潜力。这样的系统不再是一个规范的哈密顿系统，因此构造符号整合物是有问题的。在本文中，我们为这个问题提供了三个集成商。重要的是，这些方案具有近距离保存能源的良好特性。我们证明了$（p_n，x_n）\ mapsto（p_ {n+1}，x_ {n+1}）$的$（p_n，x_n）的离散符号映射存在，并且两个集成器是变异的符号符号。两组数值实验证明了这些集成剂的精确和长期收敛性，在顶级帽子密度和圆形限制的三体系统的示例中。
The dynamic equation of mass point in rotating coordinates is governed by Coriolis and centrifugal force, besides a corotating potential relative to frame. Such a system is no longer a canonical Hamiltonian system so that the construction of symplectic integrator is problematic. In this paper, we present three integrators for this question. It is significant that those schemes have the good property of near-conservation of energy. We proved that the discrete symplectic map of $(p_n, x_n) \mapsto (p_{n+1}, x_{n+1})$ in corotating coordinates exists and the two integrators are variational symplectic. Two groups of numerical experiments demonstrates the precision and long-term convergence of these integrators in the examples of corotating top-hat density and circular restricted three-body system.
