Suppose the system consists of N particles, and it has f (f ≤ 6 N) degrees of freedom. It is sufficient to use only f coordinates to give a complete description of the motion of the system, so f generalized coordinates q k , k = 1, 2,..., f are defined such that the virtual movements can be expressed in terms of these generalized coordinates. That is, δ δ r i ( q 1 , q 2 , … … , q f ; t ) , i = 1 , 2 , … … , m ; δ δ ϕ ϕ j ( q 1 , q 2 , … … , q f ; t ) , j = 1 , 2 , … … , n .