This prizewinning PhD thesis presents a general discussion of the orbital motion close to solar system small bodies (SSSBs),
which induce non-central asymmetric gravitational fields in their neighborhoods. It introduces the methods of qualitative
theory in nonlinear dynamics to the study of local/global behaviors around SSSBs. Detailed mechanical models are employed
throughout this dissertation, and specific numeric techniques are developed to compensate for the difficulties of directly
analyzing. Applying this method, several target systems, like asteroid 216 Kleopatra, are explored in great detail, and the
results prove to be both revealing and pervasive for a large group of SSSBs.