经典力学体系中广义坐标和自由度的数目

Number of Generalized Coordinates and Degree of Freedom in Classical Mechanics

确定力学系统的独立虚位移的数目叫做系统的自由度，不少著述中关于自由度的定义是错误的.由a个质点组成的力学体系，如受有k个完整约束，其广义坐标数目和自由度数目均为N=3a-k;如受有k个完整约束和r个非完整约束，其广义坐标数目为N=3a-k，而自由度的数目为N=(3a-k-r）。

Some definitions about the degree of freedom in some books are incorrect.The number of independent virtual displacement in mechanics is called degree of freedom of the system.When mechanical system composed of α particles has κ holonomic constraints, the numbers of generalized coordinates and degree of freedom are both (3α-κ) and when it has κ holonomic constraints and r nonholonomic constraints ,the number of its generalized coordinates is (3α-κ),while that of the latter is (3α-κ-r).