Hamiltonian perturbation solutions for spacecraft orbit prediction. The method of Lie transforms
The method of Lie transforms is described from the point of applications to Hamiltomian perturbation solutions for spacecraft orbit prediction. The most common orbital perturbations are discussed. Solutions to the approximations of the circular restricted three-body problem related to the Hill problem are discussed in full detail in three particular cases. The motion of a space probe about a natural satellite perturbed by the gravitational pull of the mother planet, the motion of the libration points, the coorbital motion of the (massless) orbiter and the smaller-mass primary of bigger mass are analytically solved by perturbations. Approaches to solve the Lyapunov instability problem, Hill simplified problem, tesseral effect problem, action-angle and non-singular variables problem, etc. are described. Hamiltomian perturbations by Lie transforms are discussed and applied to the Hamiltonian simplification method, Deprit's triangle problem and integrable problems. Also, the artificial satellite theory and perturbed elliptic motion are presented from the point of the Kepler problem; zonal, tesseral and lunisolar perturbations and non-conservative effects. The third part of the monography includes analytical methods to solve the relative motion problems and perturbed non-Keplerian motion problems, including the Hill problem, the motion inside Hill's sphere, the motion about the libration points, and the quasi-satellite orbit problem.
scientific article; zbMATH DE number 7353484