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## Main Question or Discussion Point

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?

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?