Constrained evolution of Hamiltonian phase space distributions in the presence of natural, non-conservative forces

Abstract

Confidence regions for spacecraft state can be constructed in phase space which encapsulate some region where there is a likelihood for the state to reside. These regions can be treated as phase space distributions or structures. Structures, such as surfaces or volumes, are constrained to preserve specific properties as they evolve in phase space under Hamiltonian dynamics. Thus, spacecraft uncertainty is then constrained by Hamiltonian flow which can provide insight into state determination. This work examines the modified constraints in the presence of non-conservative forces which relate to both probabilistic and geometric properties of the evolving uncertainty structure. The modified constraints are then derived for a Two-Body and drag environment and are shown to be valid after comparison with alternative methods. Applying the modified constraints, the constrained evolution of the confidence region is then tied to a simple physical explanation for the changing knowledge in our spacecraft state, in the atmospheric drag environment and Poynting–Robertson drag environment.