In the present paper, the analytical methods of the motion composition for moving points are clarified and discussed. The velocity and the acceleration composition formulas are derived for an arbitrarily moving reference frame by introducing the generalized coordinates. The results are compared with the common expressions in textbooks. Besides, the present authors propose a method to analyze the motion composition of moving points with the focus on the motion analysis of the entrainment point. Discussions are made on the application to a planar entrainment motion and the special features of these two kind of analytical methods.