Constructing motion primitive sets to summarize periodic orbit families and hyperbolic invariant manifolds in a multi-body system

• Published in: Celestial mechanics and dynamical astronomy Vol. 134; no. 1
• Main Authors: Smith, Thomas R., Bosanac, Natasha
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.02.2022; Springer Nature B.V
• Subjects: Aerospace engineering; Aerospace Technology and Astronautics; Astrophysics and Astroparticles; Classical Mechanics; Clustering; Complexity; Design; Dynamic models; Dynamical systems; Dynamical Systems and Ergodic Theory; Geophysics/Geodesy; Invariants; Moon; Motion stability; Multibody systems; Orbits; Original Article; Physics; Physics and Astronomy; System theory; Three body problem; Trajectories; Multi-body systems; Motion primitives; Dynamical systems theory; Clustering
• ISSN: 0923-2958; 1572-9478
• DOI: 10.1007/s10569-022-10063-x

Rapid trajectory design in multi-body systems often leverages individual arcs along natural dynamical structures that exist in an approximate dynamical model. To reduce the complexity of this analysis in a chaotic gravitational environment, a motion primitive set is constructed to represent the finite geometric, stability, and/or energetic characteristics exhibited by a set of trajectories and, therefore, support the construction of initial guesses for complex trajectories. In the absence of generalizable analytical criteria for extracting these representative solutions, a data-driven procedure is presented. Specifically, k -means and agglomerative clustering are used in conjunction with weighted evidence accumulation clustering, a form of consensus clustering, to construct sets of motion primitives in an unsupervised manner. This data-driven procedure is used to construct motion primitive sets that summarize a variety of periodic orbit families and natural trajectories along hyperbolic invariant manifolds in the Earth–Moon circular restricted three-body problem.