引用本文: 张劲夫. 点的速度和加速度合成定理的简便证明. 力学与实践, 2023, 45(4): 916-919. Zhang Jinfu. Simple proof of velocity and acceleration synthesis theorems for a moving pointnt. Mechanics in Engineering, 2023, 45(4): 916-919.
 Citation: Zhang Jinfu. Simple proof of velocity and acceleration synthesis theorems for a moving pointnt. Mechanics in Engineering, 2023, 45(4): 916-919. ## SIMPLE PROOF OF VELOCITY AND ACCELERATION SYNTHESIS THEOREMS FOR A MOVING POINTNT

• 摘要: 从动点的绝对矢径与动系上任意一点的绝对矢径之间的关系出发，通过对时间的求导运算，并结合点的速度和加速度的定义式，分别推导出动点的绝对速度与动系上任意一点的绝对速度之间的关系式以及动点的绝对加速度与动系上任意一点的绝对加速度之间的关系式，在此基础上，分别应用这两个关系式，推引出点的速度合成定理和点的加速度合成定理。定理的整个证明过程简单明了，逻辑性强，非常便于教学。

Abstract: By taking the time derivative of the relationship between the absolute position vector of a moving point and the absolute position vector of any point on a moving reference frame and using the definitions of the velocity and acceleration of point, the relationship formula between the absolute velocity of the moving point and the absolute velocity of any point on the moving frame, and the relationship formula between the absolute acceleration of the moving point and the absolute acceleration of any point on the moving frame are derived. Furthermore, by applying these formulas, velocity synthesis theorem and acceleration synthesis theorem for the moving point are derived. The whole process of proving the theorems is simple and clear, highly logical, and very easy to teach. / 下载:  全尺寸图片 幻灯片
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