New Types Of Periodic/Quasi-periodic Orbits Design And Application About Libration Points

Libration points play an important role in the field of deep space exploration.Circular Restricted Three-Body Problem has the characteristics of nonlinear and complex.At present,two different methods are used to solve the problems,constructing approximate analytic solutions and numerical methods.Constructing approximate analytic solutions will be a failure when non-linear error increases.Numerical methods can be used to solve those problems.However,Numerical methods don’t have a systematic method to calculate spacecraft orbits.A typical differential correction method,which belongs to numerical methods,is introduced to calculate the spacecraft’s orbits.Periodic orbits have symmetrical geometry structure in space.The Newton iteration method can be combined with The Bent’s method to calculate periodic orbits initial values to draw periodic orbits.Quasi-periodic orbits don’t have symmetrical geometry structure in space,so it’s difficult to calculate quasi-periodic orbits.A new method,called Time Escape Map,is proposed to calculate quasi-periodic orbits.In addition,the Poincare Section can be used to calculate the periodic orbits and quasi-periodic orbits in the plane.Axial symmetry in the plane and space plane symmetry are used to design periodic orbits.Typical Lyapunov orbits and Halo periodic orbits are found in these ways.Some new types of periodic orbits are also found in these ways.Some new types of quasi-periodic orbits are found by using 2D and 3D Time Escape Map.In the end,Characteristics about the new types of periodic orbits and quasi-periodic orbits are analyzed.The results find that the new types of orbits can be used in orbit transfer and navigation constellation.Results of simulation show that the new types of periodic orbits and quasi-periodic orbits are valuable.