I Understanding Classical Mechanics: Acceleration

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In classical mechanics, acceleration can be determined from coordinates and velocities due to the relationship defined by the equations of motion, assuming the generalized force depends solely on these variables. The discussion highlights that this dependency is a fundamental aspect of classical mechanics, enabling the calculation of acceleration without needing additional information at a single point in time. Clarification is provided that the assumption about the generalized force is crucial for this determination. The conversation also references a related question about uniquely defined accelerations, emphasizing the importance of understanding these foundational concepts. Overall, the discussion aims to clarify the reasoning behind the relationship between coordinates, velocities, and acceleration in classical mechanics.
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I'm reading once again through Landau-Lifchitz and I am stuck on the first page! I can't wrap my head around why we only need to define the coordinates and velocities to determine the acceleration? Surely if we only know those two in a single point in time, that's not enough to determine an acceleration? What am I missing here? Thanks!
 
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From the equations of motion with given ##q## and ##\dot{q}## you get ##\ddot{q}##. Of course you need the assumption that the (generalized) force depends only on ##q## and ##\dot{q}## as usual in classical mechanics.
 
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