Energetic Investment
There is an amazing fact in the old good Newtonian mechanics: you don't have to spend any energy to move a physical body(mass). If you do take into an account, that you may move it as slow, as you wish - and, nevertheless, move it, in time, as far as you need - this fact becames more intuitively acceptible. But even at high velocities, you should't really spend any energy, as it may be, in theory, fully recuperated in the end. The usual energy losses are the mere technical detail - quite irrelevant in so far, as the theory is concerned.
There are no formula, connecting the transportation of the physical body for the distance S and the energy SPENT - as there are no such connection. And, nevertheless, you should invest some energy for some time - in order to receive the change in position of the phisycal body. So, there shoul be some definite energetic characteristic to the process of locomotion. Lets find it:
S = v*t => v = S/t - where v - velocity, needed in order to move to the distance S in time t.
E = (m*v**2)/2 = (m*(S**2)/(t**2))/2 - Newtonian formula for the cynetic energy
Thus
EI = E*t**2 = (m*(S**2))/2, where EI - Energetic Investment, nessasary in order to move the mass m for the distance S. The unit of mesurement - kg*meter**2
As there are other types of locomotion but the classical mechanical(tunnel effect, probably - wormholes, etc.), I do propose the EI as the invariant for all types of locomotions. The invariants and symmetries are the first thing to look for as you study the problem - at least in so far, as the groops theory is concerned.
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