the parabolic path of a body curving under gravity.

一个物体在重力作用下的抛物线变化
If at some point this complicated object fragments into two chunks,

如果在某个点这个复杂的物体碎成两块
one will land here and one will land there.

一块落到这里一块落到那里
But at every instant, if you follow the center of mass,

但是在每个时刻如果你考察质心的运动
it'll go as if nothing happened and it will land here.

它会像不受影响一下依然落在这里
The center of mass does not care about internal forces,

质心不受内力影响
only about external forces.

仅受外力作用
That's the main point.

这就是要点
And it was designed in such a way

它天生就具有这样的性质
that external forces canceled in these dynamics.

外力在这些动力学系统中抵消了
So, everything I'm going to do today is to take that equation,

今天这堂课的主要内容就是研究这个方程
M·X two dots equal to F or M·R two dots equal to F,

M·X 两点等于 F 或者 M·R 两点等于 F