Affiliation:
1. University of Colorado Boulder, Boulder, Colorado 80303
Abstract
Natural transitions between bounded motions near mean-motion resonances occur throughout our solar system and are valuable in trajectory design. Such phenomena have been examined for natural transitions between periodic orbits near resonances within multi-body systems. However, families of quasi-periodic trajectories, tracing the surface of invariant 2-tori, significantly expand the solution space of bounded motions near resonances. Yet, identifying natural transitions between spatial 2-tori has previously been cumbersome due to the high dimensionality of the associated solution space. This paper approaches the challenge in constructing these natural transfers by using a combination of Poincaré mapping, a well-known technique from dynamical systems theory, and manifold learning, a technique for dimension reduction. The presented approach involves projecting a higher-dimensional dataset of intersections recorded from the hyperbolic invariant manifolds of two 2-tori onto a lower-dimensional embedding, enabling rapid identification of initial guesses for natural transfers. These initial guesses are then corrected and input to a continuation scheme to recover families of geometrically similar transfers connecting families of invariant 2-tori. This approach is demonstrated by constructing families of natural transitions between tori near distinct resonances in the Earth–Moon circular restricted three-body problem.
Publisher
American Institute of Aeronautics and Astronautics (AIAA)
Subject
Applied Mathematics,Electrical and Electronic Engineering,Space and Planetary Science,Aerospace Engineering,Control and Systems Engineering
Cited by
3 articles.
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