时间校正的Verlet数值积分公式(The time

时间校正的Verlet数值积分公式(The time-corrected Verlet numerical integration formula)

Johnathan Dummer在网上有一个常用的verlet集成公式，称为Time-Corrected Verlet。 不过，我读过几篇论坛帖子，人们在某些情况下会得到奇怪或意想不到的结果。

公式由Johnathan Dummer提供：

x1 = x + (x – x0) * dt / dt0 + a * dt^2

还有一个叠加的答案 ，它表明杜默的时间校正公式被打破，海报将他自己的推导作为正确的公式推出。

建议通过一个stackoverflow答案正确的公式

x1 = x + (x – x0) * dt / dt0 + a * dt * (dt + dt0) / 2

那么，Dummer的公式真的坏了吗？ 如果是的话，海报的推导是否更好？

PS：Dummer在他的网站上使用verlet积分公式x1 = x - x0 + a * dt^2而不是正确的x1 = 2x - x0 + a * dt^2也很奇怪。

There is a commonly used verlet-integration formula on the web by Johnathan Dummer, called Time-Corrected Verlet. However I've read several forum posts, that people get weird or unexpected results with it in certain conditions.

Formula by Johnathan Dummer:

x1 = x + (x – x0) * dt / dt0 + a * dt^2

There is also a stackoverflow answer, which states that Dummer's time-corrected formula is broken and the poster presents his own derivation as the correct one.

Suggested correct formula by a stackoverflow answer

x1 = x + (x – x0) * dt / dt0 + a * dt * (dt + dt0) / 2

Well, is Dummer's formula really broken? If yes, is the derivation of the poster better?

PS: It is also weird that Dummer uses the verlet integration formula x1 = x - x0 + a * dt^2 on his website instead of the correct x1 = 2x - x0 + a * dt^2.