This document reflects the effort of constructing a basis for understanding attitude motion within a multi-body problem with application to spacecraft flight dynamics. The circular restricted three-body problem (CR3BP) is employed as a model for the orbital motion.Then, attitude dynamics is discussed within the CR3BP. Conditions for bounded attitude librations and techniques for the identification of such behavior are presented: initially for a spacecraft fixed at an orbital equilibrium point, and later for a vehicle that moves on non-linear periodic orbit. While previous works focus on specific challenges, this analysis serves to create a more general framework for attitude dynamics within the CR3BP. A larger framework enables additional observations. For example, a linkage is noted between regions of bounded motion that may appear on an attitude grid search map and families of periodic attitude solutions. Finally, coupling effects between attitude and orbit dynamics within the CR3BP, ones that enable new options for trajectory design, are considered an important opportunity, and should be included in a general framework. As a proof of that concept, sailcraft trajectories are generated within a coupled orbit-attitude model only using a sequence of constant commands for the attitude actuators.
The attitude motion of a rigid spacecraft in fully nonlinear reference orbits is explored in this investigation, within the context of the planar circular restricted three-body problem. The reference trajectories originate from the Lyapunov families about the Lagrangian points L1 and L2 in the Earth–Moon system. Kane’s method is employed to derive the equations of motion, which are numerically solved. The capability to reproduce the dynamic response is leveraged to understand the attitude behavior across the Lyapunov families. The problem formulation and the simulation environment are detailed. The inertia properties of the spacecraft are varied across the periodic family of orbits. Finally, attitude maps are introduced to summarize the results and identify the regions, in terms of the orbit size and inertia properties, where the spacecraft maintains the initial orientation with respect to the rotating frame in the circular restricted three-body problem
As demonstrated by ongoing concept designs and the recent ARTEMIS mission, there is, currently, significant interest in exploiting three-body dynamics in the design of trajectories for both robotic and human missions within the Earth-Moon system. The concept of an interactive and 'dynamic' catalog of potential solutions in the Earth-Moon system is explored within this paper and analyzed as a framework to guide trajectory design. Characterizing and compiling periodic and quasi-periodic solutions that exist in the circular restricted three-body problem may offer faster and more efficient strategies for orbit design, while also delivering innovative mission design parameters for further examination.
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