# 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

### 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.**