| = | d | (p1δq1 + p2δq2 + ...) − δΤ, |
| dt |
(4)
by § 1 (14). The last member may be written
| ṗ1δq1 + p1δq˙1 + ṗ2δq2 + p2δq˙2 + ... − | ∂Τ | δq˙1 − | ∂Τ | δq1 − | ∂Τ | δq˙2 − | ∂Τ | δq2 − ... |
| ∂q˙1 | ∂q1 | ∂q˙2 | ∂q2 |
(5)
Hence, omitting the terms which cancel in virtue of § 1 (13), we find
| Σm(ẍδx + ÿδy + z¨δz) = (ṗ1 − | ∂Τ | ) δq1 + (ṗ2 − | ∂Τ | ) δq2 + ... |
| ∂q1 | ∂q2 |
(6)
For the right-hand side of (2) we have
Σ(Xδx + Yδy + Zδz) = Q1δq1 + Q2δq2 + ... ,