用复矢量证牵连运动为平面运动点加速度定理

By Complex Vector Analysis to Demonstrate the Theorem of Acceleration Composition of Articles When Carrier Motion Is Plane Motion

牵连运动为平面运动时点的加速度合成定理的证明是运动学中的一个难点．理论力学教材对该定理均未给出证明，而仅引用牵连运动为定轴转动时点的加速度合成定理的结论，这样显然不妥．本文先给出这一重要定理，然后用极坐标矢量法〔１〕（简称复矢量法）对定理进行证明．

It is a difficult point in kinematics to demonstrate the composition theorem of acceleration of particles when carrier motion is plane motion.Obviously it is not proper that all the textbooks of Theory Mechanics only introduce the statement of the theorem of acceleration composition of particles when carrier motion is the rotation round a fixed axis without giving the demonstration of it.In this paper,first this important theorem is provided and then is proved by means of complex polar coordinates vector.