| + n ( | dw | + u′ | dw | + v′ | dw | + w′ | dw | ). |
| dt | dx | dy | dz |
(3)
But as l, m, n are the direction cosines of a line fixed in space,
| dl | = mR − nQ, | dm | = nP − lR, | dn | = lQ − mP; |
| dt | dt | dt |
(4)
so that
| Dk | = l ( | du | − vR + wQ + u′ | du | + v′ | du | + w′ | du | ) + m (...) + n (...) |
| dt | dt | dx | dy | dz |
| = l ( X − | 1 | dp | ) + m ( Y − | 1 | dp | ) + n ( Z − | 1 | dp | ), | |||
| p | dx | p | dy | p | dz |
(5)
for all values of l, m, n, leading to the equations of motion with moving axes.