To address NASA's need for applying advanced dynamical theories to space mission design and analysis, especially in the context of unstable orbital trajectories in the vicinity of small bodies and libration points, Physical Optics Corporation (POC) proposes to develop a novel advanced Orbit Dynamic Computation Approach for Space Mission Analysis in the Vicinity of Small Bodies and Libration Points (ODYBOLP), with corresponding computational algorithms and software based on advanced models of complicated celestial dynamical systems with libration points (LPs) and a pseudo-arclength continuation method for computation of periodic orbits in such systems. The ODYBOLP approach will enable users to analyze space missions using: (a) all possible stable and unstable periodic orbits near LPs of Sun-Earth and Earth-Moon systems, etc.; (b) all possible periodic orbits near asteroids and comets; (c) possible dynamic transitions between different orbits connecting them to each other to organize space for near-zero fuel cost passageways through such orbits. The ODYBOLP software will be integrated into standard NASA software (GMAT, JAT, etc.) for mission analysis and design. In Phase I, POC will demonstrate the feasibility of the ODYBOLP approach. In Phase II, POC will develop a fully functional software system and demonstrate its complete feasibility.