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Consortium for Mathematics and its Applications

Product ID: 99652
Supplementary Print
Undergraduate

Spacecraft Attitude, Rotations and Quaternions (UMAP)

Author: Dennis Pence


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

©1984 by COMAP, Inc.
UMAP Module
44 pages

Mathematics Topics:

Abstract & Linear Algebra

Application Areas:

Engineering & Construction , Physical Sciences , Space Flight

Prerequisites:

Ability to compute the norm, dot product, and cross product of three-dimensional vectors; matrix representing a linear operator; orthonormalization and orthognal matrices; compute determinants, eigenvalues, and eigenvectors.

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