The building of theoretical mechanics can be constructed using only the first and the second derivatives (those of coordinates in case of kinematics: velocity and acceleration and those of energy in case of dynamics: force and gradient thereof). It is obviously unavoidable if one wants to deal with linear responses. However, it is a feature of mathematical formalism we use.(adsbygoogle = window.adsbygoogle || []).push({});

My question is whether we have any justification or proof that taking into account higher order derivatives do not lead us to deeper levels of understanding mechanics (or may be some other areas of physics whose mathematical description ist based on the 1st and the 2nd derivatives) in general case, at least in principle (it is possible of course to invent a special case where they do play some rôle, but I am not interested here in inventing such cases)?

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# I Is there place for higher order derivatives in mechanics?

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