Abstract This paper presents a unified method upon Hamiltonian description of one dimensional second order dissipative systems. In this method, the first order partial differential equation is constructed by the first integral. As long as the corresponding characteristic equation has an explicit solution, the dissipative system has an explicit Hamiltonian function. The Hamiltonians for three types of representative dissipative systems have been established and some interesting examples are given from the perspective of Hamiltonian dynamics.

中文翻译：

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通过统一方法的耗散机械系统的广义哈密顿形式

摘要 本文提出了一种对一维二阶耗散系统进行哈密顿描述的统一方法。在该方法中，一阶偏微分方程由一阶积分构成。只要对应的特征方程有显式解，耗散系统就有显式哈密顿函数。建立了三种具有代表性的耗散系统的哈密顿量，并从哈密顿动力学的角度给出了一些有趣的例子。