My homework problem is a proof in orbital mechanics, but I'm not looking for specific help on that just yet, I'd like to work through it on my own. In doing so however, I'm having a hard time conceptualizing the idea of derivatives of vectors at a specified time. If r is a general position vector, and r0 is the position vector at time t0, and the same applies for velocity vectors v and v0, it seems to me that the derivatives of each of the vectors specified at time 0 should be 0, because these values are constant. But I also don't see how that can be true because v0 should be the derivative of r0.
r=ar0+bv0 where a and b are scalar functions of time.
The Attempt at a Solution
If I attempt to take the derivative of the above equation, I'm not sure whether or not I can say the derivatives of r0 and v0 are 0, leaving me with v=a'r0+b'v0 or not.
Thanks for any help guys, sorry if this is a bit of a dumb question but it's really messing with my head right now. Cheers