Applications of Clustering to Higher-Dimensional Poincare Maps in Multi-Body Systems

摘要

Poincare maps are invaluable for rapidly analyzing the complex solution space within multi-body dynamical systems. However, for spatial motion or even planar dynamics in a nonautonomous model that does not admit a constant of motion, the information contained on a Poincare map is often higher-dimensional and, therefore, challenging to visualize. In this paper, clustering is used to group higher-dimensional crossings on a Poincare map according to the geometry of the associated trajectories; this procedure is demonstrated for natural and low-thrust-enabled solutions in the circular restricted three-body problem. The value of this clustering approach in reducing the complexity of visualization and analysis is demonstrated within the context of trajectory construction for the Lunar IceCube mission.