(1)
Since the variations δp1, δp2, ... δq1, δq2, ... may be taken to be independent, we infer the equations § 1 (23) as before, together with
| ∂T | = − | ∂T` | , | ∂T | = − | ∂T` | , ..., |
| ∂q1 | ∂q1 | ∂q2 | ∂q2 |
(2)
Hence the Lagrangian equations § 2 (14) transform into
| ṗ1 = − | ∂ | (T` + V), ṗ2 = − | ∂ | (T` + V), ... |
| ∂q1 | ∂q2 |
(3)
If we write
H = T` + V,
(4)