We address the formulation and analysis of energy and momentum conserving time integration schemes in the context of particle dynamics, and in particular atomic systems. The article identifies three critical aspects of these models that demand a careful analysis when discretized: first, the treatment of periodic boundary conditions; second, the formulation of approximations of systems with three-body interaction forces; third, their extension to atomic systems with functional potentials. These issues, and in particular their interplay with Energy-Momentum integrators, are studied in detail. Novel expressions for these time integration schemes are proposed and numerical examples are given to illustrate their performance.

中文翻译：

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分子动力学的能量-动量守恒积分方案

我们在粒子动力学的背景下，特别是原子系统中讨论能量和动量守恒时间积分方案的制定和分析。本文确定了这些模型在离散化时需要仔细分析的三个关键方面：第一，周期性边界条件的处理；第二，具有三体相互作用力的系统的近似公式；第三，它们扩展到具有功能潜力的原子系统。详细研究了这些问题，特别是它们与能量-动量积分器的相互作用。提出了这些时间积分方案的新表达式，并给出了数值例子来说明它们的性能。