速度合成定理的一种证明方法

An Approach to Prove the Theorem of Velocity Composite

指出理论力学中速度合成定理的重要性以及一些教材在证明这一定理时出现的概念问题,列举了近年来学者们对这一问题的讨论。然后将泊松公式进行推广,通过引入刚体(动系)瞬时角速度矢的概念,得到固结于做任意运动刚体上的矢量对时间一阶导数的表达式,并基于该表达式和刚体的角速度矢以及三种速度的概念给出了速度合成定理的解析证明过程。该过程逻辑严密、思路清晰,既提高了学生的逻辑思维能力,也为加速度合成定理的推导奠定了坚实的基础。

The importance of the theorem of velocity composite is pointed out.The puzzles in proving this theorem with the traditional geometrical method from current textbooks are illustrated,and domestic scholars' discussions are enumerated.By expanding on the Poisson's formula and based on the concept of instant angular velocity vector of a rigid body,the expression of the first derivative of vector versus time,which is fixed onto a mobile rigid body,is held.The analytical method for proving the theorem of velocity composite is proposed based on the expression,the instant angle velocity vector of a rigid body and concepts of three kinds of velocity.The process,logical and clear,has not only improved students' logical thinking,but also laid a solid foundation for the derivation of the theorem of acceleration synthesis.