Analytical mechanics is established based on d’Almbert-Lagrange Principle, Gauss principle, Jourdian principle and Hamilton principle, to deal with the dynamics of mechanical systems subject to holonomic or nonholonomic constraints. The governing equation of the systems are derived either by introducing Lagrange’s multipliers to adjoin with the limitation equations for the virtual displacements, or by directly eliminating the constraint equations to achieve minimal formulations. The author presents a survey for the history of analytical mechanics, and explains some basic concepts, such as virtual displacement, ideal constraint, and the correlations between the Lagrange multipliers and the real constraint forces.

%U https://xbna.pku.edu.cn/EN/10.13209/j.0479-8023.2016.082