MATLAB Quaternion (Hamilton Number) Toolbox

This toolbox is designed to facilitate quaternion (Hamilton number) operations within MATLAB. Users can efficiently perform fundamental quaternion arithmetic operations including addition, subtraction, multiplication, and division through intuitive function calls. The implementation includes specialized algorithms for handling quaternion algebra rules and non-commutative multiplication. Advanced operations such as inverse calculation, norm computation, and conjugate determination are implemented using optimized mathematical approaches with proper singularity handling. The toolbox also contains an extensive function library supporting practical applications like Euler angle to quaternion conversion (using ZYX or other rotation sequences) and quaternion to Euler angle transformation with proper singularity management. These functions employ robust numerical methods to ensure accuracy in attitude representation conversions. Additionally, the toolbox includes vector rotation operations, quaternion interpolation methods (SLERP), and differential equation solvers for quaternion kinematics. By providing optimized matrix operations and memory-efficient data structures, this toolbox significantly streamlines quaternion computation workflows and enhances user productivity in applications ranging from 3D graphics to aerospace navigation systems.