Landau Lifshitz's statement on Coordinates, velocity & acceleration

[bubba_bones]

In Landau-Lifgarbagez Classical Mech there is a statement - " Mathematically if all the coordinates 'q' and velocities 'qdot' are given at some instant, the accelerations 'q double-dot' at that instant is uniquely defined" on page 1 in Chapter - Equation of Motion. "

However, I always thought infinite values of instantaneous acceleration are possible with such a knowledge of instantaneous velocities and given coordinates , how could one say that they were unique !

Am I wrong or have I been misinterpreting the statement ?

Thanks in advance for help :)

 

[George Jones]

In Landau-Lifgarbagez Classical Mech there is a statement - " Mathematically if all the coordinates 'q' and velocities 'qdot' are given at some instant, the accelerations 'q double-dot' at that instant is uniquely defined" on page 1 in Chapter - Equation of Motion. "

However, I always thought infinite values of instantaneous acceleration are possible with such a knowledge of instantaneous velocities and given coordinates , how could one say that they were unique !

Am I wrong or have I been misinterpreting the statement ?

Thanks in advance for help :)

I'll take a stab at this, but I am not sure that I have the correct interpretation.

If the values of the coordinates and velocities at some instant are known, *and* if the equations of motion are given as a second-order differential equations, then there are unique solutions to the differential equations of motion, and thus the accelerations are uniquely defined.

 

[mordechai9]

Well, you get the accelerations from the Lagrangian, T - V, which only includes terms proportional to q and q-dot. The uniqueness of the solution will come from the theory of ODE's, like George Jones says.

Infinite instantaneous values of acceleration are not really relevant here, since they are talking about formulas like q and q-dot, not the actual numerical evaluations of those formulas.

You should probably just keep reading and see if it gets explained later. That book is written at a high level and it is hard to understand everything the authors say. (Speaking from personal experience.)