The behaviour of moving points on curves with rotating frames

In this paper, we construct rotating frames for curves, including plane curves, space curves and curves on surfaces. Hence, the behaviour of an arbitrary moving point on a curve can be seen as the composite of linear motion and rotation. Conversely, it can also prove that a curve can be determined by the two motions of its moving point, namely, linear motion and rotation. Thus, we obtain a new binary mathematical formation mechanism for curves based on the aforementioned two motions. Finally, we apply this rotating frame method to the study of the behaviour of moving points on ellipses.