Humber,
Here's one that mentions it explicitly:
"As can be expected, the solution is invariant under adding a constant to all velocities, which is like using a frame of reference with constant translational velocity."
That means energy is conserved, and is the contrary of what you hope to say. One rocket at 2V has 4 times the KE of one at V. So the collision will not be the same.
The problem Carteers have has nothing to do with frames, but a simple schoolboy error that has been made into a theory. TAD have been told countless times they have made this error, and now Prof Rhett has told them again, and with an in-your-face example from Mythbusters.
KE is quadratic with velocity, so KE =1/2mv^2 simple and linear addition is not possible.
The problem lies in very basic mistakes like this:
Consider the case of two cars passing on the highway - one northbound and the other southbound. They pass with several car widths between them. Let's say each is going 60 mph. At the moment they're adjacent to one another, their relative speed is 120 mph. But their closing speed is 0 mph at that moment.
Which is to say they could collide with no force. The speed difference is constant, and does not change. Lie the balloons, another schoolboy error.
The TM is a monumental error. Velocities may be added linearly, and that is what is meant by them being relative: there is no dependence upon some absolute frame or magnitude of the velocity ( for speeds of interest to us).
Velocity is not speed. When making the transform, one may add or subract speed
or velocity, but the latter may not be treated as speed.
If the arithmetic result changes sign an that is simply accepted, error may result. It is expected that the reader of the text knows how to handle such
math, and when the use of RMS may be a way to do that for example.
The TM is a monumental error. Taking the constant speed from from the wind, brings it to zero, but taking it from the ground, makes it negative. That is a reversal of the relationship of wind and ground that does not exist.
Dr Camp says that the making the road a belt that is moving backwards, is an invalid transform and that is the reason why.
KE + Heat = Total energy.
Total energy = KE + Work.
KE is stored energy, and work is expended energy that is not recoverable.
Joule equated heat and work long ago. Deformation, sound heat etc..all work.