| dv | = | dp | z − | dr | x + pqρ sin θ + qrρ sin θ, |
| dt | dt | dt |
(16)
| dw | = | dq | x − q2ρ cos θ. |
| dt | dt |
(17)
The dynamical equations (4)...(9) can now be reduced to
| X | = − | dq | z − p2z cotθ + q2 (x − ρ sin θ) + prx cot θ − g sin θ, |
| M | dt |
(18)
| Y | = | dp | z − | dr | x − pq (x + z cot θ − ρ sin θ) + qrp cos θ, |
| M | dt | dt |
(19)
| Z | = | dq | x + q2 (z − ρ cos θ) + p2z − prx − g cos θ, |
| M | dt |