论文标题
在Hamiltonian系统的第一个积分上，与Hamiltonian一起
On First Integrals of Hamiltonian System with Holonomic Hamiltonian
论文作者
论文摘要
在这项研究中，根据相应的汉密尔顿系统的第一个积分，研究了汉密尔顿 - 雅各比方程（HJE）的解决方案。全体函数与称为pfaffian系统的特定类型的部分微分方程有关，该方程的解决方案可以将其视为有限维真实矢量空间。在有限维解决方案空间中，定义HJE解决方案的第一积分的存在的特征是有限数二维向量的有限数量代数方程，可以易于求解和验证。通过数值示例说明了派生的表征。
In this study, the solution of the Hamilton-Jacobi equation (HJE) with holonomic Hamiltonian is investigated in terms of the first integrals of the corresponding Hamiltonian system. Holonomic functions are related to a specific type of partial differential equations called Pfaffian systems, whose solution space can be regarded as a finite-dimensional real vector space. In the finite-dimensional solution space, the existence of first integrals that define a solution of the HJE is characterized by a finite number of algebraic equations for finite-dimensional vectors, which can be easily solved and verified. The derived characterization was illustrated through a numerical example.
