TY - JOUR A2 - Vahala, Linda L. AU - Qian, Ying-Jing AU - Yang, Xiao-Dong AU - Yang, Lei-Yu AU - Zhang, Wei PY - 2016 DA - 2016/10/19 TI - Approximate Analytical Methodology for the Restricted Three-Body and Four-Body Models Based on Polynomial Series SP - 9747289 VL - 2016 AB - The restricted three-body problem (R3BP) and restricted four-body problem (R4BP) are modeled based on the rotating frame. The conservative autonomous system for the R3BP and nonautonomous system with period parametric resonance due to the fourth body are derived. From the vibrational point of view, the methodology of polynomial series is proposed to solve for these problems analytically. By introducing the polynomial series relations among the three directions of motion, the three-degree-of-freedom coupled equations are transferred into one degree-of-freedom containing the full dynamics of the original autonomous system for the R3BP. As for the R4BP case, the methodology of polynomial series combined with the iterative approach is proposed. During the iterative approach, the nonautonomous system can be treated as pseudoautonomous equation and the final polynomial series relations and one-degree-of-freedom system can be derived iteratively. SN - 1687-5966 UR - https://doi.org/10.1155/2016/9747289 DO - 10.1155/2016/9747289 JF - International Journal of Aerospace Engineering PB - Hindawi Publishing Corporation KW - ER -