Spacecraft Dynamics and Control

Welcome to AA 528: Spacecraft Dynamics and Control. This is a homepage that has evolved over a few iterations of the course.

Instructor: Taylor P. Reynolds

• The most recent course syllabus can be found here.

Lecture Notes

Here is a broad list of topics we will cover in some semblance of order. Notes and lecture videos will be added here as we go.

• Course Overview, Orbital Mechanics, Keplerian Orbits.
  • Lecture 1.a: Course Overview, Two-Body Problem
  • Lecture 1.b: Two-Body Problem, Kepler’s Laws
• Single- & Multi-Impulse Orbital Maneuvers.
  • Lecture 2: Orbital maneuvers.
• Perturbed/Non-Keplerian Orbits.
  • Lecture 3.a: Orbital Elements and General Perturbations 
  • Lecture 3.b: Gaussian VOP, Some Specific Perturbations.
• Rendezvous and Docking, Hill’s Equations, Relative Motion and Formation Flight.
  • Lecture 4: Rendezvous & Hill’s Equations.
• Mechanics of Rotations & Dynamics of Rigid Bodies.
  • Lecture 5.a: Coordinate Frames & Rotation Matrices.
  • Lecture 5.b: Attitude Parameterizations
  • Lecture 5.c: Attitude Kinematics & Dynamics.
  • Lecture 5.d: Stability of Torque-Free Motion
  • Some extra reading that might help:
    • Malcolm Shuster’s paper on the nature of quaternions.
    • This short excerpt from P.C. Hughes’ textbook.
• Spacecraft Attitude Control.
  • Lecture 6.a: Introduction to Control, Passive Control Methods.
  • Lecture 6.b: The Details of Gravity Gradients.
  • Lecture 6.c: Active Control Methods, Introduction to Linear Feedback Methods.
  • Lecture 6.d: Linear Feedback Methods I.
  • Lecture 6.e: Linear Feedback Methods II.
  • Lecture 6.f: Introduction to Nonlinear Control, Lyapunov’s Direct Method.
  • Lecture 6.g: Nonlinear Control, LaSalle’s Theorem.
• The Rest of The Loop.
  • Lecture 7.a: Sensors & Actuators.
• Special Topics
  • Lecture S.a: Apollo Powered Descent Guidance.
• Guest Lectures:
  • Lecture G.a: Introduction to Attitude Estimation (Krish Kaycee).
  • Lecture G.b: Kepler’s Laws, Newton’s Laws, and Gravitational Models (Mehran Mesbahi).

Homework

Some of the questions may contain “design” flaws the first time they were asked. These generally got worked out & updated over time, but I do apologize if any remain. I’ve included the full historical list, even if some later years repeated/re-framed/improved on certain questions from a previous year.

2019

• Homework 1.
• Homework 2.
• Homework 3.
• Homework 4.
• Homework 5.
• Homework 6.
• Homework 7.
• Homework 8.
• Homework 9.

2020

• Homework 1.
• Homework 2.
• Homework 3.
• Homework 4.
• Homework 5.

Resources

Here is a short list of constants that we will use often. This will help standardize your homework/exam answers with the ones I will use to grade them.

• (Older) introduction to orbital mechanics
• CelesTrak Astrodynamics Software by D. Vallado. A handy resource for verifying your own code.
• Companion Matlab code for Atmospheric/Space Flight Dynamics by A. Tewari.
• On attitude representations and quaternions:
  • Malcolm Shuster’s survey paper.
  • A fun historical perspective on quaternions in math and engineering.
  • A handy set of quaternion identities. (Use these identities carefully. I am not saying that our quaternion conventions will always adhere to those of the authors.)