A new theory of general planetary perturbations in rectangular coordinates is developed. Expansion of the potential in terms of multipoles and application of operator calculus yield a direct and automatic way of forming the equations for the perturbations of any order. The perturbations in the position vector are decomposed along the instantaneous position and velocity vectors of the undisturbed motion and along the normal to the plane of the undisturbed motion. This decomposition leads to a direct method of integration and final formulas that are in a convenient form for programming.
Giittingen &lit 18 .\bbiltlungcn. (Eingegangen 1968 Mai 24)In eincr Gemcinschaftsarbeit fiihrten die Autoren im Winter 1966/67 numerische ITntersuchungen iibcr Form und Verhalten periodischer Bahnen des problbme restreint im Sonne-Jupiter-System und in der Nahe der Kommensurabilitaten vom Typus (k + x)/k durch, insbesondere fur die beiden Fallc 211 (Hekuba-Liicke) und 3/2 (Hilda-Gruppe). Dic Rcchnungen wurden mit einer schnellen IBhf-Rechenanlage ausgefiihrt und ergaben neue Einsichten in die Genealogic drr periodischen L6sungen bei groI3er Annlherung an die kritischen mittleren Bewegungen. Dariiber hinaus versuchte I-. CARPENTER cine hier nicht ausfiihrlich auseinandergesetzte Thcorie, die fur Bahncn mit nicht zu groDer Exzentrizitat konvergente trigonometrische Entwicklungen ermoglicht, wobei er seine gemeinsam init P. MUSEN erarbeitete Theoric dcr allgemeinen St6rungen in rechtwinkligen Koordinaten benutzte.The authors, collaborating during the winter 1966/67, performed numerical investigations on form and character of periodic solutions of the restricted problem of three bodies in the Sun-Jupitcr-System and in the neighbourhood of the resonances of the (k + r)/k type. The principal part of these computations which wcre achieved using a fast IBMcomputer refers to the cases 211 (Hecuba-gap) and 3/2 (Hilda-group). The results gave new insight into the genealogy of periodic orbits in the regions which do not contain solutions of POINCARO'S first gcnre. Moreover, L. CARPENTER tried to develop an analytical theory (here not explicitely described) which leads to convergent trigonometric series for the coordinates of periodic orbits with restricted eccentricities, using the method of general perturbations in rectangular coordinates recently published by P. MUSEN and himself.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.