标题： 非局部力学 显示英文标题

标题： Nonlocal Mechanics

摘要： 我们引入了一个非局部拉格朗日系统的哈密顿框架，而无需依赖无限阶导数展开。 从一个（基于轨迹的）变分原理和广义诺特定理出发，我们定义了正则动量和能量。 此外，我们在运动学空间上构造了一个（预）辛形式，并表明其在相空间上的限制（通过实施约束）产生了一个真正的（预）辛结构，该结构编码了动力学。 三个例子——一个有限非局部振子、完全非局部的Pais-Uhlenbeck模型和一个延迟谐波振子——展示了如何在不显式求解欧拉-拉格朗日方程的情况下出现相空间和哈密顿量。 显示英文摘要

摘要： We introduce a Hamiltonian framework for nonlocal Lagrangian systems without relying on infinite-derivative expansions. Starting from a (trajectory-based) variational principle and a generalized Noether theorem, we define the canonical momenta and energy. Moreover, we construct a (pre)symplectic form on the kinematic space, and show that its restriction to the phase space (by implementing the constraints) yields a true (pre)symplectic structure encoding the dynamics. Three examples -- a finite nonlocal oscillator, the fully nonlocal Pais-Uhlenbeck model, and a delayed harmonic oscillator -- demonstrate how phase space and the Hamiltonian emerge without explicitly solving the Euler-Lagrange equations.