(20)
or, in the case of a conservative system
⅋ + V + K = const.,
(21)
which is the equation of energy.
The equation (16) includes § 3 (17) as a particular case, the eliminated co-ordinate being the angular co-ordinate of a rotating solid having an infinite moment of inertia.
In the particular case where the cyclic momenta κ, κ′, κ″, ... are all zero, (16) reduces to
| d | ∂⅋ | − | ∂⅋ | = Qr. | |
| dt | ∂q˙r | ∂qr |
(22)
The form is the same as in § 2, and the system now behaves, as regards the co-ordinates q1, q2, ... qm, exactly like the acyclic type there contemplated. These co-ordinates do not, however, now fix the position of every particle of the system. For example, if by suitable forces the system be brought back to its initial configuration (so far as this is defined by q1, q2, ..., qm), after performing any evolutions, the ignored co-ordinates χ, χ′, χ″, ... will not in general return to their original values.