When the motion is such that
| u = − | dφ | − m | dψ | , v = − | dφ | − m | dψ | , w = − | dφ | − m | dψ | , |
| dx | dx | dy | dy | dz | dz |
(6)
as in § 25 (1), a first integral of the equations in (5) may be written
| ∫ | dp | + V + ½q2 − | dφ | − m | dψ | + (u − u′) ( | dφ | + m | dψ | ) |
| ρ | dt | dt | dx | dx |
| + (v − v′) ( | dφ | + m | dψ | ) + (w − w′) ( | dφ | + m | dψ | ) = F(t), |
| dy | dy | dz | dz |
(7)
in which
| dφ | − (u − u′) | dφ | − (v − v′) | dφ | − (w − w′) | dφ |
| dt | dx | dy | dz |
| = | dφ | − (U − yR + zQ) | dφ | − (V − zP + xR) | dφ | − (W − xQ + yP) | dφ |
| dt | dx | dy | dz |