Comoving frames and the Lorentz–Fitzgerald contraction

In special relativity, accelerated objects are described through instantaneous comoving frames, to which the usual transformations are then applied. This is not always possible, however. I analyze a simple example of a rod thrown from a train onto a stationary platform. The lack of absolute simultaneity implies that the rod stretches, and its points move with respect to each other. Its length, therefore, changes. Typically, the rod as a whole has no instantaneous rest length and thus no definable proper length. A fortiori, it has no instantaneous rest frame, and the (instantaneous) Lorentz contraction formula is inapplicable.