dPH dPH
q`1 = ----, q`2 = ----, ..., (6)
dPp1 dPp2
which follow at once from Sec. 1 (23), since V does not involve p1, p2,
..., we obtain a complete system of differential equations _of the
first order_ for the determination of the motion.
The equation of energy is verified immediately by (5) and (6), since
these make
dH dPH dPH dPH dPH
-- = ---- p`1 + ---- p`2 + ... + ---- q`1 + ---- q`2 + ... = 0. (7)
dt dPp1 dPp2 dPq1 dPq2
The Hamiltonian transformation is extended to the case of varying
relations as follows. Instead of (4) we write