Teaching

Course Overview: In this graduate course, Dr. Canales Garcia explains fundamentals of two-body motion, conic sections, Kepler's laws, integrals of motion, universal variables formulation, and orbital maneuvers. Rigorous modeling of orbit prediction through analytical and numerical methods of computing spacecraft orbits under the influence of gravitational, aerodynamic, and other perturbing forces. Fundamentals of perturbation theory, variation of parameters, and Lagrange's planetary equations. Applications to rendezvous and space navigation.  This course also includes principles of reference frames and astronomy, principles of orbit determination and estimation, Lambert and other trajectory solvers, as well as mathematical computations using 3D spherical trigonometry.

Learning Outcomes:

• Solve two-body orbital mechanics problems 

• Solve nonlinear algebraic and differential equations using ODE45

• Analyze spacecraft orbits 

• Calculate 2D and 3D space trajectories as well as maneuvers

• Derive motion of multiple bodies under gravitational force 

• Describe relative motion between spacecraft in proximity 

• Apply filtering methods to estimate orbits based on a few observations

• Reference frames

• Orbit determination

• Spherical trigonometry

• Algorithm development

Textbook: Fundamentals of Astrodynamics and Applications 

ISBN: 9780792369035 

Authors: D.A. Vallado 

Publisher: Springer Science & Business Media 

Publication Date: 2001-06-30

Course Overview: In this graduate course designed for PhD students, students will get a theoretical and computational understanding of trajectory design of spacecrafts in the presence of two or more gravitational bodies. It includes advanced studies for the design of space missions, three-body modeling, advanced topics in computational astrodynamics, stability analysis, differential corrections, and advanced design methods in astrodynamics, such as Poincare sections and other types of maps.

Learning Outcomes:

• Analyze and solve advanced problems related to the three-body problem, including equilibrium points and stability analysis. 

• Apply numerical methods and utilize the state transition matrix for trajectory design and analysis. 

• Identify, categorize, and analyze families of periodic orbits and spacecraft transfers. 

• Implement computational algorithms and targeting schemes. 

• Utilize Poincare sections, surfaces, and other types of maps for advanced mission design. 

• Conduct stability analysis and differential corrections for improving the fidelity of mission designs. 

• Conduct research-level studies in the area of computational astrodynamics. 

• Communicate complex technical information effectively through reports and presentations.

Textbook: The Three-Body Problem and the Equations of Dynamics 

ISBN: 9783319528991 

Authors: Henri Poincaré 

Publisher: Springer 

Publication Date: 2017-05-11

Textbook: Dynamical Systems 

ISBN: 9780387495156 

Authors: Wang Sang Koon, Martin W. Lo, Jerrold E. Marsden 

Publisher: Springer 

Publication Date: 2011-06-01