## Roll Control Using Pitch and Yaw

For description purposes, imagine that the LCD thrusters provide orthogonal thrust, not angled thrust. We can make a 90 degree roll with a 90 degree yaw, a 90 degree pitch, and a 90 degree yaw again, like so:

A 180 degree pitch, followed by a 180 degree yaw, causes a 180 degree roll. Smaller rotations can be accomplished with smaller pitches and yaws.

The same process applies to the derivatives, so it is possible to create a continuous spin in the roll direction by adding spin in yaw, then spin in pitch, then add spin in yaw again to create spin in the roll direction. This will be complicated by sun angle and the actual force vectors, and will also result in translations in relation to the array, so the exact maneuver will need to be carefully computed in advance. Fortunately, thinsats think a lot faster than they move.

The moment of inertia for flipping end over end is I = 0.25 M R^{2}, while the moment of inertia for rotating flat is I = 0.50 M R^{2} . Thus, the lowest energy rotation for a given angular momentum is rotating flat.

See Rotation for more details, including stopping a spinning thinsat.