标题： 从运动方程确定哈密顿量及实例说明 显示英文标题

标题： Determination of the Hamiltonian from the Equations of Motion with Illustration from Examples

摘要： 在本文中，我们研究从给定的运动方程确定哈密顿量的问题。在将系统重新解释为相空间坐标中的第一阶演化方程后，这个问题可以转化为矩阵分解问题。我们给出了存在哈密顿量的演化矩阵的标准。此外，证明是构造性的，可以得到一个带有伴随辛结构的显式哈密顿量。作为应用，我们将研究一些动力系统类别以进行说明。 显示英文摘要

摘要： In this paper, we study the determination of Hamiltonian from a given equations of motion. It can be cast into a problem of matrix factorization after reinterpretation of the system as first-order evolutionary equations in the phase space coordinates. We state the criterion on the evolution matrix for a Hamiltonian to exist. In addition, the proof is constructive and an explicit Hamiltonian with accompanied symplectic structure can be obtained. As an application, we will study a few classes of dynamical systems for illustration.