- #1

LukasMont

- 6

- 3

"If all the co-ordinates and velocities are simultaneously specified, it is known from experience that the state of the system is completely determined and that its subsequent motion can, in principle, be calculated. Mathematically this means that, if all the co-ordinates q and q˙ are given at some instant, the accelerations q¨ at that instant are uniquely defined".

I don't understand how that can be the case. Knowing the positions and velocities in a given moment allow me to calculate the new positions at a dt time afterwards, if accelerations are all zero. If not, I'll need to know the accelerations from some other source, like knowing the forces acting on the system, etc. I don't see how merely having positions and accelerations in a given moment gives you the accelerations in that moment as well.