| Σm(ẋδx + ẏδy + z˙δz) = | ∂Τ | δq1 + | ∂Τ | δq2 + ... |
| ∂q˙1 | ∂q˙2 |
(9)
This maybe regarded as the cardinal formula in Lagrange’s method. For the right-hand side of (3) we may write
Σ(X′δx + Y′δy + Z′δz) = Q′1δq1 + Q′2δq2 + ... ,
(10)
where
| Q′r = Σ(X′ | ∂x | + Y′ | ∂y | + Z′ | ∂z | ). |
| ∂qr | ∂qr | ∂qr |
(11)
The quantities Q1, Q2, ... are called the generalized components of impulse. Comparing (9) and (10), we have, since the variations δq1, δq2,... are independent,
| ∂Τ | = Q′1, | ∂Τ | = Q′2, ... |
| ∂q˙1 | ∂q˙2 |