Application of Kane's method to incorporate attitude dynamics into the circular restricted three-body problem
Abstract
The three-dimensional, nonlinear, coupled orbit and attitude motion of a spacecraft in both planar and spatial reference orbits is explored in this investigation, within the context of the Circular Restricted Three-Body Problem (CR3BP). The motion of a multibody spacecraft, comprised of two rigid bodies connected by a single degree of freedom joint, under the gravitational influence of the Earth and the Moon is examined. Kane's dynamical formulation is employed and a model framework to develop the fully coupled orbit and attitude differential equations that govern spacecraft motion in the CR3BP is realized. The nonlinear variational form of the equations of motion is employed to mitigate numerical effects arising from large discrepancies in the length scales. Within this framework, a process is summarized with steps for implementation resulting in a series of coupled nonlinear equations of motion for the complex spacecraft model. Several nonlinear, periodic reference orbits in the vicinity of the collinear libration points are selected for further investigation and the effects of the orbit on the orientation, as well as the orientation on the orbit, are examined. Attitude maps are employed to summarize the results; the inertia properties of the spacecraft are varied across a periodic family of reference orbits in the vicinity of the collinear libration points. These maps indicate regions, in terms of the orbit size and inertia properties, where the spacecraft maintains the initial orientation with respect to the circular restricted three-body rotating frame. Reference orbits for the system include both planar Lyapunov orbits and three-dimensional halo trajectories. Additionally, the model is extended to include solar radiation pressure and the motion of a solar sail type spacecraft is examined.
Degree
Ph.D.
Advisors
Howell, Purdue University.
Subject Area
Aerospace engineering
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