论文标题
结构保留时间归档化的汉密尔顿系统的离散化，并适用于非自主力学
Structure preserving discretization of time-reparametrized Hamiltonian systems with application to nonholonomic mechanics
论文作者
论文摘要
我们提出了对矢量场的离散化，这些载体场是哈密顿量，直至通过相位空间上的正函数乘以乘法，这可以解释为时间重新分析。我们证明，我们的方法是在某种意义上通过具有相同结构的连续系统的流动来插值到任意顺序的意义上。特别是，我们的离散化保留了对任意顺序的相空间的平稳度量。我们向一类杰出的非体力学机械系统提供了应用，该系统允许汉密尔顿化。据我们所知，这些结果提供了文献中的第一次措施，即保留了保存非卫生系统的措施离散化。
We propose a discretization of vector fields that are Hamiltonian up to multiplication by a positive function on the phase space that may be interpreted as a time reparametrization. We prove that our method is structure preserving in the sense that the discrete flow is interpolated to arbitrary order by the flow of a continuous system possessing the same structure. In particular, our discretization preserves a smooth measure on the phase space to arbitrary order. We present applications to a remarkable class of nonholonomic mechanical systems that allow Hamiltonization. To our best knowledge, these results provide the first occurrence in the literature of a measure preserving discretization of measure preserving nonholonomic systems.
