关于可变质量的椭圆型限制性三体问题运动方程的再探讨

ON FURTHER RESEARCH FOR EQUATIONS OF MOTION FOR ELLIPTIC RESTRICTED PROBLEM OF THREE BODIES WITH VARIABLE MASS

较近期的关于可变质量的椭圆型限制性三体问题的运动方程[5]是对于n=1的情况,本文把星序数n扩充到2,3及4,对于每一种n,分别建立了可变质量的椭圆型限制性三体问题的运动方程。

The equations of motion of elliptic restricted problem of three bodies with variable mass according to n =1(k = 0, q =1/2) were derived more recently[5]. We have expanded the main sequence star to n = 2(k = 1, q = 3/2), n = 3(k = 2, q = 6/2) and n = 4(k = 3, q = 7/2) in this paper. For each case we established each set of differential equations of motion with variable mass. On the other hand, we corrected some errors in the previous work forn=1(k = 0, q=1/2), which still possess an effect on the simplified form of differential equations of motion for problem of three bodies with variable mass although they are non-substantial. The three sets of differential equations of motion for elliptic restricted problem of three bodies are indicated in Formulae (41), (42) and (43) corresponding to n = 2, n = 3 and n = 4, respectively.