and therefore by (48)
| (51) | dq | = | dq | dt | = | rv | . |
| di | dt | di | g |
It is convenient to express r as a function of v in the previous notation
(52) Cr = f(v),
and now
| (53) | dq | = | vf(v) | , |
| di | Cg |
an equation connecting q and i.
Now, since v = g sec i
| (54) | dt | = -C | sec i | , |
| dq | f(q sec i) |
and multiplying by dx/dt or q,