Thesis - Leigh Moody.pdf - Bad Request - Cranfield University

Appendix I / Utilities
_ _
Matrix Product (Post-Multiplier Transposed)
Matrix Product (Pre & Post Transposed)
Matrix Subtraction
Matrix Trace
22.1.9 Quaternion Utilities
CMS group [ QUATERNIONS ]
22.1-6
Matrix of Correlation Coefficients
Matrix Eigen Analysis
Matrix Insertion
Matrix Extraction
These utilities manipulate quaternions in the context of frames, time rate of
change, and gradients with respect to their individual scalar and vector
components.
Quaternion Conjugation
YPR Euler Angles to Quaternions
Quaternion Product
Quaternion Normalisation
Quaternion Propagation
Quaternion Error Propagation
22.1.10 Trigonometric Functions
CMS group [ TRIG ]
Quaternion Propagation by Euler Angle Increments
Quaternion Transformation Matrix
Quaternion Vector Transform
Quaternion from Direction Cosines
Direction Cosine Jacobians
When developing algorithms the host mathematical library is usually the
source of the trigonometrical functions used. For application software faster
computation of these functions is often required, albeit with a reduced
accuracy. These utilities give a reasonable level of accuracy with minimal
computational effort.
Sine Approximation
Cosine Approximation
Tangent Approximation
Arc-sine Approximation
22.1.11 Vector utilities
CMS group [ VECTORS ]
Arc-cosine Approximation
Arc-tangent Approximation (Single Argument)
Arc-tangent Approximation (Two Arguments)
These utilities complement the matrix utilities, although the latter are often
used a dimension set to one. Vector utilities have a lower computational
loop overhead and are design so that a subset of a vector can be manipulated
in isolation.
Angle Between Vectors Vector X-Z Magnitude