# Can you determine acceleration from positions and velocities only?

I just began reading the Landau and Lifshitz book on classical mechanics. It states on the first page of Chapter 1 that:

Mathematically, this means that, if all the coordinates $q$ and velocities $\dot{q}$ are given at some instant of time, the accelerations $\ddot{q}$ at that instant are uniquely defined.

For given positions and velocities of a system of particles at a given instant, can't each particle have an arbitrary acceleration? Also, aren't accelerations determined from forces?

• Can you be more precise about where it says this, and maybe provide the quote along with context? – Mike May 5 '15 at 12:55
• Oh, bottom of page 1, I guess. – Mike May 5 '15 at 12:59
• @Mike Yup, that's right – IanDsouza May 5 '15 at 13:04
• Your last sentence is the key here - given positions, velocities, and the equations for the forces in the system, the accelerations will be uniquely defined. No, the particles can not have arbitrary accelerations - they must have the accelerations as defined by the classical mechanics at play in the situation. – Jon Custer May 5 '15 at 13:44
• Related: physics.stackexchange.com/q/18588/2451 , physics.stackexchange.com/q/4102/2451 and links therein. – Qmechanic May 5 '15 at 16:18