How does classical mechanics change if motion was not infinitely differentiable?

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Many "theoretical mechanicians" seem to awesome that motion is a [tex]{C^\infty }[/tex] function(at least that is how I learned it). However, it seems like the postulates of Newtonian/Lagrangian/Hamiltonian/Vakonomic mechanics seem to "work" in the general case where only the motion is a [tex]{C^2}[/tex](ie the acceleration always exists, but the jerk does not).

My question is how classical mechanics would change if we assume the general case where the motion of a particle is only guaranteed to be twice differentiable? Are there any MAJOR changes?
 

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Andy Resnick
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Good question. My guess is 'no'. The Langevin equation (Brownian motion) results in perfectly reasonable physics.
 
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Are you talking about "Achilles and the tortoise" and Zeno's paradoxes?
 

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