- #1
TheCanadian
- 367
- 13
Just using basic dimensional analysis, it appears the time derivative of centripetal acceleration is ## \vec{r} \omega^3 ##, but this intuitive guess would also extend to higher order time derivatives, no? Implying:
## \frac {d^n \vec{r}}{dt^n} = \vec{r} \omega^n ##
It seems to follow from the general result shown in Thorton/Marion pg 390 (attached) when considering rotating bodies in a fixed frame. I assume ## \vec{Q} ## is any vector, even ones that are the result of a higher order time derivative of an initial vector. The concept of finite infinite-time derivative just seems like an odd concept to me when considering real objects, but I guess the geometry of the situation allows it. But to confirm, is anything posted here incorrect?
## \frac {d^n \vec{r}}{dt^n} = \vec{r} \omega^n ##
It seems to follow from the general result shown in Thorton/Marion pg 390 (attached) when considering rotating bodies in a fixed frame. I assume ## \vec{Q} ## is any vector, even ones that are the result of a higher order time derivative of an initial vector. The concept of finite infinite-time derivative just seems like an odd concept to me when considering real objects, but I guess the geometry of the situation allows it. But to confirm, is anything posted here incorrect?