Advanced Orbital Dynamics
Learning Objective:Introduce students to spacecraft orbital dynamics and the issues associated with orbital design and stationkeeping in regimes where multiple gravitational fields are simultaneously significance. Thus, primary focus is the three body problem and regimes where two-body analysis and conics are not valid models. Numerical methods to support trajectory design including differential corrections strategies. Families of solutions and their stability analysis.
Discussion of more advanced concepts in astrodynamics. Includes fundamental theories from celestial mechanics, resonance, dynamical systems theory and numerical methods with application to the motion in multi-body regimes and interplanetary spacecraft under the simultaneous influence of multiple gravitational bodies. Assumes experience with the two-body problem.
Topics Covered:1. Review of the two-body problem and response
2. Introduction to the three-body problem; equilibrium points and stability
3. Numerical methods and the state transition matrix
Families of periodic orbits
5. Introduction to maps and surfaces of section
6. Invariant manifolds and transfer design