Then we find the Hamiltonian in its two forms, with the help of 4-velocity and the generalized momentum, and substitute the Hamiltonian into Hamilton equations to verify the motion equations.
However, the specified quantities in the first approximation are independent from the 4-velocity of the substance unit.
We shall note that from the definition of 4-velocity [u.
In (34) and (35) the Hamiltonian is expressed through the 4-velocity [u.
The Hamiltonian (64) can be represented in another form by using the generalized 4-velocity (66).
This applies to the value of the generalized 4-velocity of the substance unit, and the total momentum of the substance and fields.
The difference between the masses m and M is due to the fact that at the addition of substance units into a coherent body the 4-velocity [u.
Hamiltonian, expressed through the 4-velocity and characterizing the energy of the particle (substance unit) with mass m, is given by (34).