2⅋ = Σm (ẋ² + ẏ² + z˙²), 2Τ0 = ω²Σm (x² + y²),
(24)
| αr = Σm (x | ∂y | − y | ∂x | ), |
| ∂qr | ∂qr |
(25)
whence
| (r, s) = 2ω·Σm | ∂(x, y) | . |
| ∂(qs, qr) |
(26)
The conditions of relative equilibrium are given by (23).
It will be noticed that this expression V − T0, which is to be stationary, differs from the true potential energy by a term which represents the potential energy of the system in relation to fictitious “centrifugal forces.” The question of stability of relative equilibrium will be noticed later (§ 6).
It should be observed that the remarkable formula (20) may in the present case be obtained directly as follows. From (15) and (14) we find