(25)
K may also be expressed as a homogeneous quadratic function of the cyclic velocities χ˙, χ˙′, χ˙″,... Denoting it in this form by Τ0, we have
δ (T0 + K) = 2δK = δ (κχ˙ + κ′χ˙′ + κ″χ˙″ + ...)
(26)
Performing the variations, and omitting the terms which cancel by (2) and (25), we find
| ∂Τ0 | = − | ∂K | , | ∂Τ0 | = − | ∂K | , ..., |
| ∂q1 | ∂q1 | ∂q2 | ∂q2 |
(27)
so that the formulae (23) become
| Q1 = − | ∂Τ0 | , Q2 = − | ∂Τ0 | , ... |
| ∂q1 | ∂q2 |
(28)