Spacecraft Attitude, Rotations and Quaternions (UMAP)

This module applies linear algebra to space flight and astrophysics. The rotational orientation of a spacecraft is called the attitude. Attitude can be represented by a matrix, a vector and an angle, or a sequence of angles. One of the more interesting representations uses quaternions. This module explores quaternion algebra and the relationships between these representations.

Table of Contents:

INTRODUCTION

ATTITUDE MATRIX
Definition
Direction Cosine Matrix
Transition Matrix
Proper Orthogonal Matrix
Rotation Operator
Euler Angle Sequences

QUATERNION ALGEBRA
Historical Development
Vector Space Properties
Quaternion Product
Further Properties

QUATERNION ROTATION OPERATOR
Definition
Properties
Representation for Attitude

KINEMATIC EQUATIONS FOR ATTITUDE
Dynamics and Kinematics
Quaternion Kinematics
Attitude Matrix Kinematics
Euler Angle Kinematics

BIBLIOGRAPHY

ACKNOWLEDGMENT

MODEL EXAMINATION

ANSWERS TO EXERCISES

ANSWERS TO MODEL EXAM