Wednesday, 2 September 2015

Analytical Solution with Two Time Scales of Circular Restricted Three-Body Problem



Analytical Solution with Two Time Scales of Circular Restricted Three-Body Problem
F.B. Gao1, H.L. Hu2

1School of Mathematical Science, Yangzhou University, Yangzhou 225002, China
2College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, China


Abstract Analytical solution performs a vital role in a wide variety of deep space exploration missions, especially the periodic solutions which were believed to be the unique avenue to solve three-body problem by PoincarĂ©. As the absence of a general solution for the problem, an approximate analytical solution of the circular restricted three-body problem is addressed by employing multiple scales method in conjunction with some analytical techniques. It is worthwhile to note that the presented solution in three-dimensional space contains two time scales:  and  ( is a small, dimensionless parameter), which is significative to improve and perfect the known literature.
Keywords Analytical solution, multiple scales, three-body problem.

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