For the particular case of an elastic multibody system (MBS) that can be modeled using one-dimensional finite elements, the main methods offered by analytical mechanics in its classical form for analysis are presented in a unitary description. The aim of the work is to present in a unitary form the main methods offered by classical mechanics for the analysis of solid systems. There is also a review of the literature that uses and highlights these methods, which need to be reconsidered considering the progress of the industry and the complexity of the studied systems. Thus, the kinematics of a finite element is described for the calculation of the main quantities used in the modeling of multibody systems and in analytical mechanics. The main methods used in the research of MBS systems are presented and analyzed. Thus, Lagrange’s equations, Gibbs–Appell equations, Maggi’s formalism, Kane’s equations and Hamilton’s equations are studied in turn. This presentation is determined by the advantages that alternatives to Lagrange’s equations can offer, which currently represent the method most used by researchers.

对于可以使用一维有限元建模的弹性多体系统（MBS）的特殊情况，分析力学以其经典形式提供的主要分析方法以统一的描述形式呈现。这项工作的目的是以统一的形式呈现经典力学为固体系统分析提供的主要方法。还有对使用和强调这些方法的文献进行了回顾，考虑到行业的进步和所研究系统的复杂性，需要重新考虑这些方法。因此，有限元运动学被描述用于计算多体系统建模和分析力学中使用的主要量。介绍并分析了MBS系统研究中使用的主要方法。因此，依次研究了拉格朗日方程、吉布斯-阿佩尔方程、马吉形式主义、凯恩方程和汉密尔顿方程。本演示是由拉格朗日方程的替代方法可以提供的优点决定的，拉格朗日方程是目前研究人员最常用的方法。