- #1
ngawang
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In Landau's Mechanics it states "If all co-ordinates and velocities are simultaneously specified, it is know 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 [itex]q[/itex] and velocities [itex]\dot{q}[/itex] are given at some instant, the accelerations [itex]\ddot{q}[/itex] at that instant are uniquely defined."
My question is why is this so. I understand that from knowing the co-ordinates of a mechancial system the future evolution of a system is not uniquely determined. But how does the additional knowledge of the velocities uniquely determine the acceleration of the system and hence its future mechanical state?
My question is why is this so. I understand that from knowing the co-ordinates of a mechancial system the future evolution of a system is not uniquely determined. But how does the additional knowledge of the velocities uniquely determine the acceleration of the system and hence its future mechanical state?