如果還沒讀過

• [14 min] n01_dynamics_overview.ipynb

 

是時候了！

此處擷取其中一段文本，講兩個『參考系定位』之『觀點約定』︰

 

否則困惑恐生也？

Active and passive transformation

In physics and engineering, an active transformation, or alibi transformation,^[1] is a transformation which actually changes the physical position of a point, or rigid body, which can be defined even in the absence of a coordinate system; whereas a passive transformation, or alias transformation,^[2] is merely a change in the coordinate system in which the object is described (change of coordinate map, orchange of basis). By default, by transformation, mathematicians usually refer to active transformations, while physicists and engineers could mean either.

Put differently, a passive transformation refers to description of the same object in two different coordinate systems.^[3] On the other hand, an active transformation is a transformation of one or more objects with respect to the same coordinate system. For instance, active transformations are useful to describe successive positions of a rigid body. On the other hand, passive transformations may be useful in human motion analysis to observe the motion of the tibia relative to the femur, that is, its motion relative to a (local) coordinate system which moves together with the femur, rather than a (global) coordinate system which is fixed to the floor.^[3]

In the active transformation (left), a point moves from position P to P’ by rotating clockwise by an angle θ about the origin of the coordinate system. In the passive transformation (right), point P does not move, while the coordinate system rotates counterclockwise by an angle θ about its origin. The coordinates of P’ in the active case (that is, relative to the original coordinate system) are the same as the coordinates of P relative to the rotated coordinate system.