基于瞬时角速度矢和角加速度矢的合成运动定理的证明

Proof of the Theorems in Synthetic Motion of Points Based on Instant Vectors of Angular Velocity and Angular Acceleration

首先将泊松公式推广,通过引入刚体(动系)瞬时角速度矢和瞬时角加速度矢的概念,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,并基于该表达式及刚体的角速度矢和角加速度矢以及三种速度和加速度的概念给出了速度和加速度合成定理的解析证明过程。

By extending the Poisson＇s formula, and introducing the concepts of instant angular velocity vector andaccerlation vector of a rigid body, expression of the first derivative of a vector fixed witha rigid body movingarbitrarily was obtained. And, the procession of analytical method for proving the composite theorems of velocity andacceleration was proposed based on the expression, the instant angle vectors of velocity and acceleration of a rigid bodyand concepts of three kinds of velocity and acceleration.