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Newton's second law usually is written:

$$F(t,x,\dot{x})=m\ddot{x}$$

Why not to allow forces which depend on higher derivatives? Is there any principle hidden?

Is it the same reason why lagrangians of higher order aren't considered? I mean, usually it is said that you can give up higher derivatives redefining variables...Does it include non-local forces with infinite number of derivatives?

In summary, is there any physical principle why forces which depend on higher derivatives, or even negative order or fractional order derivatives are not included in the common physical expositions and formulations of classical mechanics and newton's laws?

riemannium
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  • I'm pretty sure this is a duplicate. I just don't remember where exactly I saw it. Did you check around on the site for similar questions already? – hft Aug 29 '22 at 18:05
  • For example: https://physics.stackexchange.com/q/154456/ – hft Aug 29 '22 at 18:06
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    Lots of previous questions about it. I'll add one more, with the refenerces you can find therein https://physics.stackexchange.com/q/175545/ – basics Aug 29 '22 at 18:08
  • https://physics.stackexchange.com/questions/4102/why-are-there-only-derivatives-to-the-first-order-in-the-lagrangian – hft Aug 29 '22 at 18:10

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