(12)
These are the general equations of impulsive motion.
It is now usual to write
| pr = | ∂Τ | . |
| ∂q˙r |
(13)
The quantities p1, p2, ... represent the effects of the several component impulses on the system, and are therefore called the generalized components of momentum. In terms of them we have
Σm(ẋδx + ẏδy + z˙δz) = p1δq1 + p2δq2 + ...
(14)
Also, since Τ is a homogeneous quadratic function of the velocities q˙1, q˙2 ...,
2Τ = p1q˙1 + p2q˙2 + ...