推导加速度合成公式的“牵连点跟踪法”1）

理论力学是大学工科各专业本科生的技术基础课，点的合成运动是重点与难点内容之一。部分学生对牵连（加）速度，特别是对（加）速度合成定理的推导需要较长时间才能理解和适应。很多教材（如文献1,2]）都引入了“牵连点”的概念。牵连点的定义为：某瞬时与动点重合的动系上的点称为动点在该瞬时的牵连点。由于动点相对动系有运动，不同的瞬时动点与动系上不同的点重合，因此不同瞬时的牵连点是不同的。某瞬时的牵连（加）速度就是该瞬时的牵连点相对定系的（加）速度。牵连点的引入能较好地帮助学生理解牵连（加）速度。在定理推导的教学实践中，虽然用目前的教材中所采用的方法都能很好地证明该定理，但我们注意到，“两点”（即牵连点与动点）在时间点和空间位置上的“重叠性”会给学生带来理解和掌握的难度，学生容易在“重叠性”这一点上产生困惑。文献3]就动系做定轴转动，采用了一种将动点从其重合点“拉开”的方式，对该定理进行了推导，对解决学生的困惑有一定帮助。以下，本文以文献3]的方法为基础，补充引入“牵连点”、“绝对和相对导数”等重要概念，并就动系做一般运动对该定理进行推导，在表达方式上也做了一些调整。本文称这种推导方式为“牵连点跟踪法”。

Derivation of the Theorem on the Composition of Acceleration by the "Tracking Method of Carrier Point" 1）

In the teaching of Theoretical Mechanics, A method through tracking "carrier point" can be adopted to derive the Theorem on the Composition of Acceleration. The carrier point of a given instant is separated from the moving particle at the same space position. From the origins of fixed and moving reference system, two radius vectors are introduced to the moving particle respectively. In order to track the carrier point at any time, another two radius vectors are also introduced to the carrier point from the two origins simultaneously. Then an equation, expressing the relationship between the four radius vectors mentioned above, is differentiated with respect to the time. Both a velocity-relation expression and an acceleration-relation expression are obtained after differentiating the equation. Thus, the Theorem on the Composition of Acceleration(and Velocity) can be educed by just substituting the two expressions with the condition of carrier point. The method represented above is intuitionistic and idiographic, and all related physical quantities are easily discriminated from each other. It is convenient for students to comprehend the theorem.