Editing Spacecraft flight dynamics (section)

====Change of plane====
Plane change maneuvers can be performed alone or in conjunction with other orbit adjustments. For a pure rotation plane change maneuver, consisting only of a change in the inclination of the orbit, the specific angular momentum, ''h'', of the initial and final orbits are equal in magnitude but not in direction. Therefore, the change in specific angular momentum can be written as:
<math display="block">\Delta h = 2h\sin\left(\frac {|\Delta i|}{2} \right)</math>
where ''h'' is the specific angular momentum before the plane change, and Δ''i'' is the desired change in the inclination angle. From this it can be shown{{sfnp|Hintz|2015|p=112}} that the required delta-''v'' is:
<math display="block">\Delta v = \frac {2h\sin\frac {|\Delta i|}{2}}{r}</math>

From the definition of ''h'', this can also be written as:
<math display="block">\Delta v = 2v\cos \varphi\sin\left(\frac {\left|\Delta i\right|} 2 \right)</math>
where ''v'' is the magnitude of velocity before plane change and ''φ'' is the flight path angle. Using the [[small-angle approximation]], this becomes:
<math display="block">\Delta v = v \cos(\varphi) \left|\Delta i\right|</math>

The total delta-''v'' for a combined maneuver can be calculated by a vector addition of the pure rotation delta-''v'' and the delta-''v'' for the other planned orbital change.