and this, in conjunction with
| (46) tan i = | dy | = | dy | / | dx | , |
| dx | dt | dt |
| (47) sec2 i | di | = | ( | dx | d2y | - | dy | d2x | ) | / | ( | dx | ) | 2 , | ||
| dt | dt | dt2 | dt | dt2 | dt |
reduces to
| (48) | di | = | -g | cos i, or | d tan i | = | -g | , |
| dt | v | dt | v cos i |
the equation obtained, as in (18), by resolving normally in the trajectory, but di now denoting the increment of i in the increment of time dt.
Denoting dx/dt, the horizontal component of the velocity, by q, so that
(49) v cos i = q,
equation (43) becomes
(50) dq/dt = -r cos i,