An Object-Oriented Operator-Overloaded Quaternion Toolbox

Abstract

A Fortran 95 Object-Oriented Operator-Overloaded Toolbox is presented for automating engineering and scientific applications involving quaternion algebra. The Toolbox supports basic math operations (+,-,*,/,**), standard library functions (sin, asin, exp, ln, ....), linear equations, quadratic polynomials, and matrix-vector operations for solving linear matrix equations, matrix inversion, and eigenvalue/eigenvector operations. Extensive use is made operator-overloading and generic operators for automating the often tedious calculations required for manipulating quaternion objects. A further advantage of this approach is that conventional programming language constructs are used for developing math models, which reduces programming errors. Two strategies are presented for enabling matrix capabilities: (1) re-writing core algorithms to reflect the noncommunitive behavior of quaternions, and (2) mapping quaternion matrices to higher-dimensional complex-valued matrices. The aim of the package is to facilitate and encourage further research relying on quaternion algebraic computations for applications in dynamics, control, and optimization. Numerical examples are presented for demonstrating the basic computational capabilities of the software.