Using symplectic geometry to constrain motion in astrodynamics problems
Oliver Boodram
University of Colorado Boulder
Studying the ebb and flow of regions within an orbital environment is important for the problems of orbital uncertainty propagation and particle transport. Particle clouds, discretizing the region, can be mapped forwards to understand the shape and size of the region. To gain insight into orbital uncertainty propagation and particle transport, this presentation investigates various shape and size constraints that can be placed on evolving volumes of space. Such constraints leverage invariants from Hamiltonian mechanics and symplectic geometry. This allows us to semi-analytically approximate the likelihood that a volume stretches or transitions to different neighbourhoods of cislunar space. In addition, some constraints can be generalized to dissipative, non-Hamiltonian systems. We can then analytically probe the evolution of phase space volumes under atmospheric drag as well as under propulsion intelligently designed to collapse or expand regions of orbital uncertainty.