标题： 哈密顿处理非保守系统 显示英文标题

标题： Hamiltonian treatment of non-conservative systems

摘要： 我们提出了一种将哈密顿力学扩展到非保守系统的新型方法，该方法建立在施温格-凯尔迪什-加利双变量作用原理之上。 从加利的初始值作用出发，我们澄清了关于边界条件、物理极限轨迹的出现以及拉格朗日量分解为保守和耗散部分的重要细节。 重要的是，我们证明了冗余的双倍配置空间在规范动量层面上具有规范自由度，这不会改变物理动力学。 通过勒让德变换，我们构建了相应的相关非保守哈密顿量族；我们表明几乎任何经典的初始值问题都可以嵌入到我们扩展的辛流形中，并显式地提供了相关的哈密顿量和拉格朗日函数。 作为进一步的贡献，我们推导出了双变量作用和哈密顿量的完全等价的线性“李”形式，这简化了计算并使该形式的许多结构特性变得清晰。 显示英文摘要

摘要： We present a novel extension of Hamiltonian mechanics to nonconservative systems built upon the Schwinger-Keldysh-Galley double-variable action principle. Departing from Galley's initial-value action, we clarify important subtleties regarding boundary conditions, the emergence of the physical-limit trajectory, and the decomposition of the Lagrangian into conservative and dissipative sectors. Importantly, we demonstrate that the redundant doubled configuration space admits a gauge freedom at the level of the canonical momenta that leaves the physical dynamics unchanged. From a Legendre transform, we construct the corresponding family of gauge-related nonconservative Hamiltonians; we show that virtually any classical initial-value problem can be embedded on our enlarged symplectic manifold, supplying the associated Hamiltonian and Lagrangian functions explicitly. As a further contribution, we derive a completely equivalent linear ``Lie'' formulation of the double-variable action and Hamiltonian which streamlines computations and renders transparent many structural properties of the formalism.