| X = | dx1 | − x2 | dT | + x3 | dT | , Y = ..., Z = ..., |
| dt | dy3 | dy2 |
(3)
| L = | dy1 | − y2 | dT | + y3 | dT | − x2 | dT | + x3 | dT | , M = ..., N = ..., |
| dt | dy3 | dy2 | dx3 | dx2 |
(4)
where X, Y, Z, L, M, N denote components of external applied force on the body.
These equations are proved by taking a line fixed in space, whose direction cosines are l, m, n, then
| dl | = mR − nQ, | dm | = nP − lR, | dn | = lQ − mP. |
| dt | dt | dt |
(5)
If P denotes the resultant linear impulse or momentum in this direction
P = lx1 + mx2 + nx3,