APPLICATIONS OF SYMPLECTIC TOPOLOGY TO ORBIT UNCERTAINTY AND SPACECRAFT NAVIGATION

摘要

Gromov’s symplectic non-squeezing theorem, a fundamental property from symplectic topology, is applied to the study of uncertainty analysis in Hamiltonian Dynamical systems with a particular emphasis on spacecraft trajectory uncertainty. Previous results published in the literature are re-derived and shown to be similar to the uncertainty principle of quantum mechanics. The application of Gromov’s Theorem to uncertainty distributions in Hamiltonian Dynamical systems are discussed, including the effect of time mapping and measurement updates. Finally, we provide constraint relations on the phase volume of a distribution and the Gromov width.