⅋ + V − T0 = const.
(21)
The conditions that the equations (17) should be satisfied by zero values of the velocities q˙1, q˙2, ... q˙n are
| Qr = − | ∂T0 | , |
| ∂qr |
(22)
or in the case of conservative forces
| ∂ | (V − T0) = 0, |
| ∂qr |
(23)
i.e. the value of V − Τ0 must be stationary.
We may apply this to the case of a system whose configuration relative to axes rotating with constant angular velocity (ω) is defined by means of the n co-ordinates q1, q2, ... qn. Rotating axes. This is important on account of its bearing on the kinetic theory of the tides. Since the Cartesian co-ordinates x, y, z of any particle m of the system relative to the moving axes are functions of q1, q2, ... qn, of the form § 1 (1), we have, by (15)