The purpose of this paper is to perform an error analysis of the variational integrators of mechanical systems subject to external forcing. Essentially, we prove that when a discretization of contact order $r$ of the Lagrangian and force are used, the integrator has the same contact order. Our analysis is performed first for discrete forced mechanical systems defined over $TQ$, where we study the existence of flows, the construction and properties of discrete exact systems and the contact order of the flows (variational integrators) in terms of the contact order of the original systems. Then we use those results to derive the corresponding analysis for the analogous forced systems defined over $Q\times Q$.

翻译：本文的目的是对受到外部压力的机械系统变异集成器进行错误分析。基本上,我们证明,在使用拉格朗加亚和武力分解的接触顺序时,该集成器具有相同的联系顺序。我们的分析首先针对定义超过$Q的离散强制机械系统,我们从原始系统的接触顺序的角度研究流动、离散精确系统的构造和特性以及流动(变异集成器)的接触顺序。然后,我们利用这些结果来得出对限定在$Q的类似强制系统的相应分析。