Newton's law are invariant only when transformed from one inertial frame to another. Galilean transformation connect inertial frames, which would mean (if I understand your notation right) that $du/dt=0$.

Well... one of those derivatives will be 0. I don't quite understand why you need three accelerating frames... but Galilean transformation do not transform quantities between accelerated frames.

Newton's law are invariant only when transformed from one inertial frame to another. Galilean transformation connect inertial frames, which would mean (if I understand your notation right) that $du/dt=0$.

Well... one of those derivatives will be 0. I don't quite understand why you need three accelerating frames... but Galilean transformations do not transform quantities between accelerated frames.

Newton's law are invariant only when transformed from one inertial frame to another.

Newton's law are invariant only when transformed from one inertial frame to another. Galilean transformation connect inertial frames, which would mean (if I understand your notation right) that $du/dt=0$.

Well... one of those derivatives will be 0. I don't quite understand why you need three accelerating frames... but Galilean transformation do not transform quantities between accelerated frames.