(27)
Since the variations δq1, δq2, ... δqm, δκ, δκ′, δκ″, ... may be taken to be independent, we have
| p1 = | ∂Τ | = | ∂R | , p2 = | ∂Τ | = | ∂R | , ... |
| ∂q˙1 | ∂q˙1 | ∂q˙2 | ∂q˙2 |
(28)
and
| χ˙ = − | ∂R | , χ˙′ = − | ∂R | , χ˙″ = − | ∂R | , ... |
| ∂κ | ∂κ′ | ∂κ″ |
(29)
An important property of the present transformation is that, when expressed in terms of the new variables, the kinetic energy is the sum of two homogeneous quadratic functions, thus
Τ = ⅋ + K,
(30)