My research project
Application of high-order numerical methods to restricted three-body problem
Human deep-space explorations has become dominant in current space programs, which presents an even higher demand on the deep-space trajectory design. In order to eliminate the restrictions introduced by the two-body approximation method imposed on trajectory design, the circular restricted three-body problem (CRTBP) was investigated as the fundamental dynamics to increase the availability of more various interplanetary orbits. However, due to its high nonlinearity, most conclusions and methods related with the CRTBP are derived from linearized dynamics, which inevitably incurs limitations and inaccuracy in the application. In my research, by means of Differential Algebra techniques, high-order methods are explored and applied to the nonlinear problems related with the CRTBP. Specifically, three representative problems are targeted, including stationkeeping of libration point orbits, computation of periodic/quasi-periodic orbits, and instability and bifurcation analysis.