This question already has an answer here:
The equation of linear motion in a given coordinate axis (say $x$) in my text book:
And throughout my mechanics course I never encountered derivative with power higher than 2 in EOM?
Why is it so?
Does additional derivatives put on any restriction in a physical sense which although mathematically constructable but not physically possible? (just like imaginary roots in quadratic equation in certain problems had imaginary or negative roots of time)
EDIT: It turns out that there exist two anser which adresses the problem in terms of lagrangian mechanics
Is there any equivalent explanation from the point of view of Newtonian Dynamics?