Abstract: In the present invention, an imaginary aircraft, called the “shadow aircraft,” flies the original flight plan and, in turn, causes the true aircraft to fly the offset course. The offset course has the same number of legs as the original course, and for each leg of the original course, there is a corresponding parallel leg of the offset course. Except for an initial waypoint and a final waypoint, the locations of offset course waypoints are defined to be the intersections of the straight lines parallel to the original legs at the specified offset distance. The range and bearing to the offset course initial waypoint are chosen to be the same as the range and bearing to the next waypoint. For the interior legs of the flight plan, the lengths of the offset course legs vary from the corresponding “true” course leg.

Abstract: Stable reference gyroscopic apparatus is provided in the form of an angular displacement sensor which employs an end-supported vibratory rod or wire, instead of the commonly used rotatable element. The apparatus of the invention incorporates an improved means for maintaining the vibrational amplitude of the center of the vibratory element constant, and electronic circuit means for causing the orbit of center of the vibratory element to remain in a straight line, both means being effective to eliminate the major sources of potential drift in the sensor.