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Advanced Orbital Dynamics


Credit Hours:


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


AAE 50700, 53200

Applied / Theory:

Web Address:


Homework problems will be posted to Blackboard approximately once every two weeks.


No exams for course.


Official textbook information is now listed in the Schedule of Classes. No course materials are required for this section.

Computer Requirements:

ProEd Minimum Computer Requirements. Matlab is generally useful, but not required for developing scripts/programs.

Other Requirements:

Necessary Background <br> 1. Calculus and differential equations through ODE'S <br> 2. Vector mechanics; orbital mechanics; rigid body kinematics and dynamics; three-dimensional coordinate systems and transformations <br> 3. Some introduction to perturbation and stability analysis as well as linear algebra <br> 4. Numerical methods and tools such as MATLAB

ProEd Minimum Requirements: