When considering equations such as the Vlasov equation, the particle distribution, $f$, is taken to be a function of time, position, and velocity. But why are higher-order time-derivatives such as acceleration and jerk not considered? And why are the original set of variables considered complete and independent of one another?
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to some extent, a dup. of Why are differential equations for fields in physics of order two? and links therein. – AccidentalFourierTransform May 28 '18 at 20:27
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Related, by OP: https://physics.stackexchange.com/q/408627/25301 – Kyle Kanos May 28 '18 at 20:35
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2This is due to the least action principle. When you solve the variation of the functional, you get the Lagrange equations that depend only on position and velocity, but not on acceleration or higher derivatives. This implies that acceleration and higher derivatives are not independent functions, but are determined by position and velocity. This in turn is a reflection of the fact that the process happens in space and time represented respectively by position and velocity. No extra types of dimensions exist that would make acceleration etc. independent. – safesphere May 28 '18 at 21:25
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1@safesphere It would be great if you elaborated that and turned it into an answer. – user45664 May 28 '18 at 22:56