1. through 17 contain a sampling of the various solutions which are available. Early investigations by Danby1-4 for elliptic and hyperbolic reference orbits led to general solut'ons in universa 1 variables by Battin 5, Goodyearft,and Pitkin 7. The solution developed by Goodyear, in particular, has become a widely accepted technique for generating numerical results. Later papers by Pitkine, Pines and Fang 9, and Soong and PaullO included expressions for both the first and second partial derivatives. Major theoretical papers have been presented by Deprit and Deprit-Bartholomell, and Brouckel 2. A later update to this work is due to Hitzll 3. While the details of the results vary, all of the preceding work shares the common thread of expressing the results relative to an inertial Cartesian coordinate frame.
2. California Institute of Technology, under NASA Contract NAS7-100. **Technical Group Supervisor, Member AIAA.
3. Somewhat in parallel with these developments, investigations have been conducted where the results are expressed relative to a rotating coordinate system. The most used results relating perturbations relative to a circular arbit, were first developed by H i l l (1878) and much later rediscovered by Clohessy and Wiltshire 14 in 1960. Further work to extend the range of validity was given by Londonl 5 and Anthony and Sasakil 6.
4. .* 26 ir + 6'6r + 6s - 0 6s = - 6s (1)